Sum of Exterior Angles of a Polygon

Q.

What is the measure of any exterior angle of a regular octagon?

1. ${135}^{\circ }$

2. ${45}^{\circ }$

3. ${90}^{\circ }$

4. ${105}^{\circ }$

Q.

The figure shows a regular pentagon and a regular hexagon put together. The measure of $\angle PQR$ is

1. ${122}^{\circ }$

2. ${132}^{\circ }$

3. ${142}^{\circ }$

4. ${152}^{\circ }$

Q.

$ABCD$ is a square and $ABRS$ is a rhombus. if $\angle SAD={120}^{\circ }$,

find: (¡) $\angle ASD$ (¡¡) $\angle SRB$

Q.

In the given figure, find the angle measure x.

Q.

The given figure shows a sqaure, a regular pentagon and a regular hexagon put together. The measure of $\angle BAC$ is

1. ${22}^{\circ }$

2. ${32}^{\circ }$

3. ${42}^{\circ }$

4. ${52}^{\circ }$

Q.

If the sum of the interior angles of a regular polygon is five times the sum of its exterior angles, then the number of sides it has is

1. 10

2. 14

3. 11

4. 12

Q.

The sum of exterior angles of a polygon (in degrees) with 10 sides is

___.

Q.

If the difference between an exterior angle of an (n - 1) sided regular polygon and an (n + 1) sided regular polygon is $9^{\circ }$, the value of ‘n’ is

1. 9

2. 8

3. 10

4. 6

Q. If a regular polygon has 55 sides, then the sum of its exterior angles is ${360}^{\circ }$.

1. 
2. 

Q.

In the given figure, sides AB and CD of the quadrilateral ABCD are produced. Then the value of x is

1. ${75}^{\circ }$

2. ${80}^{\circ }$

3. ${70}^{\circ }$

4. ${65}^{\circ }$

Q.

If the ratio of the exterior angle and interior angle of a regular polygon is 2: 3, the number of sides of the polygon is

1. 7

2. 6

3. 5

4. 4

Q. In a parallelogram ABCD, determine the sum of angles $\angle B,\angle C$ and $\angle D$ if $\angle A={60}^{\circ }$ [2 MARKS]

Q.

The sum of all exterior angles of a polygon is ______ degrees.

1. 360

2. 720

3. 180

4. 540

Q. Question 1(vi)
Find the value of the unknown exterior angle x in the following diagrams:

Q. The ratio of an interior angle to the exterior angle of a regular polygon is $7:2$. Find the number of sides of the polygon.

1. $19$
2. $7$
3. $9$
4. $8$

Q.

The given figure shows a sqaure, a regular pentagon and a regular hexagon put together, which of the following statements is true?

1. $\angle P={42}^{\circ },\angle Q={69}^{\circ },\angle R={69}^{\circ }$

2. $\angle P={40}^{\circ },\angle Q={60}^{\circ },\angle R={80}^{\circ }$

3. $\angle P={46}^{\circ },\angle Q={67}^{\circ },\angle R={67}^{\circ }$

4. $△PQR$ is isosceles.

Q. What is pentagon?

Q.

In the figure, a regular octagon and a regular pentagon are put together. The measure of $\angle ABC$ is

Q.

(a) find x + y + z

(b) find x + y + z + w

Q. The regular polygon whose exterior angle is ${40}^{\circ }$ is a

1. Nonagon
2. Decagon
3. Octagon
4. Heptagon

Q.

A quadrilateral MIST where MI = 3.5 cm, IS = 6.5 cm, Angle M = ${75}^{\circ }$, Angle I = ${105}^{\circ }$ and Angle S = ${120}^{\circ }$ can exist.

1. True

2. False

Q. The value of y in the given figure is

Q. Arrange the following regular polygon in ascending order as per the measure of their external angles.

1. Triangle
2. Hexagon
3. Quadrilateral
4. Pentagon

Q. Find the measure of each exterior angle of a regular polygon of $9$ sides.

Q. Find the angle measure x in the following figure:

Q.

Find $\angle ABF$ from the given figure.

Q. Question 103
State whether the statements are True or False.
If the sum of interior angles is double the sum of exterior angles taken in an order of a polygon, then it is a hexagon.

Q.

The regular polygon whose exterior angle is ${40}^{\circ }$ is

1. Decagon

2. Octagon

3. Heptagon

4. Nonagon

Q. Question 145
In rectangle PAIR, find $\angle ARI,\angle RMI$ and $\angle PMA$.

Q. Find the number of degrees in each exterior angle of a regular pentagon.​