# The Measure Of An Exterior Angle At The Vertex Of A Polygon Equals The Measure Of The Adjacent Interior (2023)

Mathematics High School

Polygon: A polygon is a simple closed curve entirely made up of line segments.

1. As starting from triangle

Three kind of triangles: Isosceles, Scalene , and equilateral triangle

In none of these measure of an exterior angle at the vertex of the triangle equals the measure of the adjacent interior angle.

2. Quadrilateral = Parallelogram, Rhombus, Rectangle, Square, Kite, Trpzm

Apart from Rectangle and Square none other quadrilateral have The measure of an exterior angle at the vertex of the quadrilateral equals the measure of the adjacent interior angle.

we can also consider other polygons also like pentagon,hexagon,heptagon.

Decagon and found that it is not always possible that measure of an exterior angle at the vertex of a polygon equals the measure of the adjacent interior angle.

So, the correct option is Sometimes.

So an exterior angle at the vertex of a polygon not can being never equal the measure of the adjacent interior angle

## Related Questions

A sphere-shaped water balloon can extend to a diameter of 3.5 inches before it explodes. How much water can the water balloon hold before it explodes.

Use 3.14 for π.

179.5 in3

5.6 in3

21.98 in3

22.44 in3

Volume of a spehere=(4/3)πr³

Data:
diameter=3.5 in
π=3.14

r=diameter/2=3.5 in / 2=1.75 in

2) we calculate the volume of this sphere:
volume=(4/3)*3.14*(1.75 in)³=22.4379...in³≈22.44 in³.

Step-by-step explanation:

I just did the quiz.

Which expression is equivalent to 2(m − 4) + 1? 2m − 7

2m − 3

2m + 9

2m + 10

2(m - 4) + 1 = 2m - 8 + 1 = 2m - 7

The expression 2(m − 4) + 1 is equivalent to 2m - 7 .

Step-by-step explanation:

As the expression given in the question is as follows

= 2(m − 4) + 1

Now first open the bracket of the above experession

= 2m - 8 + 1

(Video) Exterior Angle Theorem For Triangles, Practice Problems - Geometry

Simplify the above

= 2m - 7

Therefore the expression 2(m − 4) + 1 is equivalent to 2m - 7 .

The diameter of a men's basketball is 24.2 centimeters. Compute the volume of the men's basketball.

Use 3.14 for π.

1854.2 cm3

5562.7 cm3

7416.94 cm3

59,335.5 cm3

To solve for the volume of the sphere given its diameter use,

V = (πd^3) / 6

Substituting the given in the problem to the equation,

V = (3.14 x 24.2^3) / 6 = 7416.94 cm^3

Thus, the answer is7416.94 cm^3 which isthe third among the choices.

Step-by-step explanation:

I just did the quiz

Factor completely 4xy + 9x + 24y + 54. I am pretty sure this is D but i would appreciate if someone checks me!

A. (4y − 9)(x − 6)
B. (4y − 9)(x + 6)
C. (4y + 9)(x − 6)
D.(4y + 9)(x + 6)

(D ) ( 4y + 9 ) ( x + 6 ) is correct option.

Step-by-step explanation:

Given : 4xy + 9x + 24y + 54.

To find : Factor completely.

Solution : We have given that 4xy + 9x + 24y + 54.

Interchanging the terms 9x and 24 y.

4xy + 24y + 9x + 54.

Taking common 4 y from first two terms and 9 from last two terms .

4 y ( x + 6 ) + 9 ( x + 6 )

On grouping

( 4y + 9 ) ( x + 6 ).

Therefore, (D ) ( 4y + 9 ) ( x + 6 ) is correct option.

(x+6)(4y+9) yes it is D.

Which statement models this situation? The distance between two cars must be greater than 45 feet.

A.
d = 45

B.
d + 45 > 0

C.
d < 45

D.
d > 45

The distance d must be greater than 45 feet
so this mean d > 45 ft

result choice D. is right sure

Factor completely 3bx2 − 9x3 − b + 3x. (b − 3x)(3x2 − 1)
(b + 3x)(3x2 + 1)
(b + 3x)(3x2 − 1)
Prime

(Video) Finding Interior and Exterior Angles in a Polygon

Hello,

3bx²-9x^3-b+3x=b(3x²-1)-3x(3x²-1)=(3x²-1)(b-3x)

a is correct ty

Step-by-step explanation:

Isabella observed that everyone on her soccer team is older than 13. She wrote the inequality a > 13 to represent the possible ages of her teammates. Which numbers satisfy the inequality but make no sense in this situation?

Choose all answers that are correct.

A.
102

B.
96

C.
15

D.
13

Of all the choices presented above, only letter D. 13 does not satisfy the inequality as the number should be higher than 13. Out of the choices that satisfy the inequality, only letter C. makes sense. Letter A and B satisfy the inequality but do not makes sense as this represent the ages of very old people already which are not capable of playing the sports.

Thus, the answer is letter A. 102 and letter B. 96.

Will upvote response and like any user that helps!! Factor completely 10xy + 3y + 20ax + 6a.

(10x − 3)(y − 2a)
(10x − 3)(y + 2a)
(10x + 3)(y + 2a)
(10x + 3)(y − 2a)

Factor completely 5ab + 3ay + 5b + 3y.

(5b + 3y)(a + 1)
(5b − 3y)(a + 1)
(5b + 3y)(a − 1)
Prime

Hello,

10xy+3y+20ax+6a=y(10x+3)+2a(10x+3)
=(10x+3)(y+2a)

5ab+3ay+5b+3y=a(5b+3y)+1(5b+3y)
=(5b+3y)(a+1)

A printer can print 30 pages in 2.5 minutes. ￼Write and solve a proportion to find the number of pages that the printer can print in 5 minutes. Show your work

The number of pages the printer can print and time are directly proportional. If we let x be the number of pages and t the time, this direct variation may be mathematically expressed as,

x = kt

where k is the constant of variation.

Substituting the given to the equation,

30 = k(2.5) ; k = 12

Solving for the number of pages printed after 5 minutes,

x = (12)(5) = 60

Thus, the printer can print 60 pages in 5 minutes.

What is the length of a side of a cube with a volume of 216 in3?

Hello,
Side=∛216=6 (in)
===========

What are the solutions of the equation x4 – 5x2 – 14 = 0? Use factoring to solve.

We will use factoring:
x² - 7 = 0
x² = 7
x =
or x=
x² +2 = 0
x² = -2, this part of equation has no solutions.

d on edge.

Step-by-step explanation:

(Video) How to find the measure of one exterior angle of a regular polygon

The surface area of a rectangular prism is 5600 mm2. What is the surface area of this prism, measured in cm2?

A.
0.56 cm2

B.
56,000 cm2

C.
56 cm2

D.
560 cm2

To answer the problem above, use conversion factor and dimensional analysis. Every centimeters is composed of 10 millimeters. Hence, every cm^2 is composed of 100 mm^2. Solving the given,

5600 mm^2 x (1 cm^2/ 100 mm^2) = 56 cm^2.

Thus, the answer is 56 cm^2 which is letter C.

Part 2: Create a scenario for a geometric sequence. For example, Anthony goes to the gym for ______ minutes on Monday. Every day he _________his gym time by ____________. If he continues this pattern, how many minutes will he spend at the gym on the 5th day? Be sure to fill in the blanks with the words that will create a geometric sequence. Use your scenario to write the formula for the 5th term in your sequence using sequence notation.

An example scenario is:

Anthony goes to the gym for 20 minutes on Monday. Every day he multiplies his gym time by 2.

On the fifth day, he will spend spend 320 minutes in the gym.

The formula used to determine the 5th term is,

a5 = 20 x 2^(r -1)

where r is the common ratio equal to 2.

The volume of a prism is 35 cm3. What is the volume of this prism, measured in mm3?

A.
0.035 mm3

B.
350 mm3

C.
35,000 mm3

D.
3.5 mm3

D. 3.5 mm3
Hope this helps!!!

Part 1: Create a scenario for an arithmetic sequence. For example, Jasmine practices the piano for ______ minutes on Monday. Every day she ___________ her practice time by _________. If she continues this pattern, how many minutes will she practice on the 7th day? Be sure to fill in the blanks with the words that will create an arithmetic sequence. Use your scenario to write the function for the 7th term in your sequence using sequence notation.

The example scenario is:

Jasmine, practices the piano for 20 minutes on Monday. Every day she increases her practice time by 20 minutes.

On the 7th day, Jasmine will spend 140 minutes practicing her piano.

The equation used to determine the 7th term is,

a7 = 20 + (7 - 1) x d

where d is the common difference, 20.

A triangle is graphed in the coordinate plane. The vertices of the triangle have coordinates (-4,1)(1,1), and (1,-11). What is the perimeter of the triangle? A. 30
B.17
C. 25
D. 18

To answer the question above, determine the distance between the points which are the vertices of the triangle.

(Video) Learn how to determine the missing value using the exterior angles of a polygon ex

1. Between (-4,1) and (1,1) ; d1 = sqrt ((1-1)² + (1--4)²) = 5
2. Between (-4,1) and (1,-11) ; d2 = sqrt ((-11-1)² +(1--4)²) = 13
3. Between (1,1) and (1,-11) ; d3 = sqrt ((-11-1)² + (1-1)²) = 12

The perimeter is the sum of the three distances. Thus, the perimeter of the triangle is 30. The answer is letter A.

Choose the product. -6p3(3p2 + 5p - 1) -18p5 - 30p4 + 6p3 -18p6 - 30p3 - 6p 18p3 + 6p2 - 30p4 -18p6 - 24p3

-6p^3(3p^2 +5p -1) = -18p^5 -30p^4 +6p^3

so this is the right answer sure

-18p^5 -30p^4 +6p^3

Determine the solution set of (x - 7)2 - 144 = 0

Taking square root on both sides,
x-7= 12
or
x-7 = -12

x=19
or
x= -5

Estimate 5.9 * 3.4

This is because 5.9 is closer to 6 than 5, so 6 *3.4
Next step: 3.4 is closer to 3 than 4 because it is not 3.5 or over.

Step-by-step explanation:

Since, We know that,

5.9 is closer to 6,

,

And, 3.4 is closer to 3,

Here, the given expression,

Hence, the value of is about 18.

Option C is correct.

Find the common difference for the given sequence. 1.05, 1.1, 1.15, 1.2, ... 0.005 0.05 0.5

Step-by-step explanation:

In the given sequence, the first term = 1.05

The second term = 1.1

The difference between first and second term =

The third term = 1.15

The difference between second and third term =

The fourth term = 1.2

The difference between third and fourth term =

Hence, the common difference of the given sequence =0.05

Given a sequence; a₁,a₂,a₃...,an,
The common difference is d= a₂-a₁=a₃-a₂=a₄-a₃....

In this case:
a₁=1.05
a₂=1.1

d=a₂-a₁=(1.1)-(1.05)=0.05

Answer: The common difference is 0.05.

## FAQs

### The Measure Of An Exterior Angle At The Vertex Of A Polygon Equals The Measure Of The Adjacent Interior? ›

The measure of an exterior angle at the vertex of a polygon equals the measure of the adjacent interior angle. Sometimes. This happens in the case of squares and rectangles.

What is the exterior angle at a vertex of polygon? ›

An exterior angle of a polygon is an angle at a vertex of the polygon, outside the polygon, formed by one side and the extension of an adjacent side. Notice that corresponding interior and exterior angles are supplementary (add to 180°). Exterior angles of a regular polygon are equal in measure.

What is the measure of the exterior angles of a polygon? ›

The sum of the exterior angles of a polygon is 360°. The formula for calculating the size of an exterior angle in a regular polygon is: 360 number of sides. If you know the exterior angle you can find the interior angle using the formula: interior angle + exterior angle = 180°

What does the measure of the exterior angle at a vertex of the vertices of an equilateral triangle equal? ›

The exterior angles of an equilateral triangle will always have a measure of 120°.

Is the measure of the exterior angle equal to the measure of its angle? ›

The measure of an exterior angle of a triangle is equal to the sum of the measures of the adjacent interior angles.

Is the measure of an exterior angle at a vertex equal to the opposite interior angle in a cyclic quadrilateral? ›

A cyclic quadrilateral is a four-sided polygon whose vertices are inscribed on a circle. In a cyclic quadrilateral, the measures of opposite angles are supplementary, an exterior angle is equal to the interior angle at the opposite vertex.

What are exterior and interior angles at a vertex? ›

An exterior angle of a triangle is the angle formed outside the triangle between any side and the extension of another side. Both exterior angles at a vertex of a triangle are congruent. An interior angle in a triangle and an adjacent exterior angle are supplementary.

What is the exterior and interior angles of a polygon? ›

The formula for calculating the size of an interior angle is: interior angle of a polygon = sum of interior angles ÷ number of sides. The sum of exterior angles of a polygon is 360°. The formula for calculating the size of an exterior angle is: exterior angle of a polygon = 360 ÷ number of sides.

What is the measure of the angle at vertex? ›

Properties. A vertex angle in a polygon is often measured on the interior side of the vertex. For any simple n-gon, the sum of the interior angles is π(n − 2) radians or 180(n − 2) degrees.

Are exterior angle at each vertex in a triangle equal? ›

Only in the case of an Equilateral triangle, the exterior angles formed at each vertex of a triangle will be equal. Therefore, the exterior angles formed at each vertex of a triangle may or may not be equal, depending on the type of the triangle.

### What is the measure of an exterior angle of a triangle is always? ›

Exterior angle is always equal to the sum of the opposite interior angles. Exterior angle is always greater than the either of the two remote interior angles.

Is the measure of the exterior angle of any polygon is equal to the sum of its remote interior angles? ›

The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two remote interior angles of the triangle. The exterior angle inequality theorem states that the measure of any exterior angle of a triangle is greater than either of the opposite interior angles.

Is the vertex a point in the exterior of an angle? ›

We know from the definition that vertex is the point of angle which is the common point of the two lines or rays which forms an angle. So here the vertex is point \$O\$. From the above figure we can see that the vertex \$O\$ neither lies in the interior nor the outside. It is on the angle.

What is the measure of an exterior angle formed at any of the vertices of a regular pentagon? ›

Exterior Angle of a Regular Pentagon

The measure of each exterior angle of a pentagon = 360°/n = 360°/5 = 72°.

Is an exterior angle of a polygon is supplementary to the interior angle at the vertex? ›

Exterior Angles

An exterior angle on a polygon is formed by extending one of the sides of the polygon outside of the polygon, thus creating an angle supplementary to the interior angle at that vertex.

What is the sum of interior and exterior angle at a vertex of a polygon? ›

The sum of the internal angle and the external angle on the same vertex is 180°.

How many exterior angles are at each vertex of the triangle? ›

A triangle has 3 sides, 3 vertices, at these each vertices, we get 2 exterior angles, therefore, 3×2=6 exterior angles.

Is the exterior angle of a polygon half the interior angle? ›

Answer and Explanation: The polygon is a hexagon.

What is the measure of each exterior angle of a polygon of a regular polygon of 9 sides? ›

1 exterior angle = 360° ÷ 9 = 40° Q.

Is a vertex angle 180 degrees? ›

A straight angle's vertex angle is 180° in measure.

### What is the measure of an angle with vertex on the center of the circle? ›

A central angle is an angle with its vertex at the center of a circle, with its sides containing two radii of the circle. In the figure above, ∠PZQ,∠QZR , and ∠RZP are central angles. Sum of Central Angles: The sum of the measures of the central angles of a circle with no points in common is 360° .

Does the exterior of a triangle equal 180? ›

One exterior angle of a triangle is equal to the sum of the other two angles in the triangle. The exterior angle is obtained by extending the side of the triangle. Since it is a straight line, the angle is 180 ° .

Is the exterior angle of a triangle is equal to the sum of two is? ›

Hence, An exterior angle of a triangle is equal to the sum of two opposite interior angles.

Are the exterior angles at a vertex of a triangle? ›

Are the exterior angles formed at each vertex of a triangle equal? No, The exterior angle formed at the vertices of a triangle are not equal. The exterior angle is equal to the sum of the two opposite interior angles.

Is an exterior angle of a triangle equal to the adjacent interior angle? ›

The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles of the triangle.

Is the exterior angle of a triangle equal to its interior adjacent angle? ›

The sum of an exterior angle of a triangle and its adjacent angle is always 180∘, because they form a linear pair.

Is the exterior angle of a triangle equal to its interior angle *? ›

An exterior angle of a triangle is equal to the sum of the two interior opposite angles.

Does the exterior of a triangle equal 360? ›

Angles on a straight line equal 180 degrees. Adding the three exterior angles or multiplying 120 by three gives us 360 degrees. Therefore, the sum of the measures of the exterior angles of an equilateral triangle are 360 degrees. This fact is also true for any triangle.

What is the exterior of exterior angle of a triangle? ›

What is the exterior angle of a triangle? The angle created by one side of a triangle and the subsequent extended side is known as the external angle of a triangle. A triangle has three exterior angles, and the sum of those three external angles is always 360 degrees.

What do vertex angles equal? ›

Vertical angles are always congruent and equal. Vertical angles are congruent as the two pairs of non-adjacent angles formed by intersecting two lines superimpose on each other.

## Videos

1. Find the Measure of the EXTERIOR ANGLE | Triangle Exterior Angle Theorem | Geometry
2. 6.1b Polygon Exterior Angle Measures
(Marshematics)
3. Determine the measure of each exterior angle of a regular octagon
(Brian McLogan)
4. Exterior Angle Theorem - Triangle Inequalities @MathTeacherGon
(Math Teacher Gon)
5. 7.1 Angles of Polygons
(Geometry with Mr. J)
6. Exterior Angle is Sum of Remote Interior Angles
(Anil Kumar)
Top Articles
Latest Posts
Article information

Author: Rev. Leonie Wyman

Last Updated: 27/09/2023

Views: 6114

Rating: 4.9 / 5 (59 voted)

Author information

Name: Rev. Leonie Wyman

Birthday: 1993-07-01

Address: Suite 763 6272 Lang Bypass, New Xochitlport, VT 72704-3308

Phone: +22014484519944

Job: Banking Officer

Hobby: Sailing, Gaming, Basketball, Calligraphy, Mycology, Astronomy, Juggling

Introduction: My name is Rev. Leonie Wyman, I am a colorful, tasty, splendid, fair, witty, gorgeous, splendid person who loves writing and wants to share my knowledge and understanding with you.