## Exercise 3.2

Question 1: Find x in the following figures.

Solution: We know that sum of exterior angles of a polygon = 360⁰
So, 125° + 125° + x = 360°
Or, 250° + x = 360°
Or, x = 360° = 250° = 110°

Solution:

We know that sum of exterior angles of a polygon = 360⁰
So, 70° + x + 90° + 60° + 90° = 360°
Or, 310° + x = 360°
Or, x = 360° - 310° = 50°

Question 2: Find the measure of each exterior angle of a regular polygon of

(i) 9 sides

Solution: Since, 9 sides of a polygon has nine angles
And we know that sum of exterior angles of a polygon = 360⁰
So, 9 exterior angles = 360°
Or, 1 exterior angle = 360°÷9 = 40°

(ii) 15 sides

Solution: Since, 15 sides of a polygon has 15 angles
And we know that sum of exterior angles of a polygon = 360⁰
So, 15 exterior angles = 360°
Or, 1 exterior angle = 360°÷15 = 24°

Question 3: How many sides does a regular polygon have if the measure of an exterior angle is 24⁰?

Solution:We know that number of angles of a polygon = number of sides
And we know that sum of exterior angles of a polygon = 360⁰
So, measure of each angle = 24°
Or, number of exterior angles = 360°÷24° = 15
Hence, number of sides = 15

Question 4: How many sides does a regular polygon have if each of its interior angles is 165⁰?

Solution: Here, each interior angle = 165°
Hence, each exterior angle = 180° - 165° = 15°
As, measure of each exterior angle = 15°
So, number of sides = 360°÷15° = 24
Hence, number of sides = 24

Question 5: (a) Is it possible to have regular polygon with measure of each exterior angle as 22⁰?

Solution:
Since, number of sides of a polygon = 360°/each exterior angle
Hence, number of sides of given polygon = 360°÷22° = 16.36

Since, answer is not a whole number, thus, a regular polygon with measure of each exterior angle as 22⁰ is not possible.

(b) Can it be an interior angle of a regular polygon? Why?

Solution: Here, each interior angle = 22°
Hence, each exterior angle = 180° - 22° = 158°
Hence, number of sides = 360°÷158° = 2.27

Since, answer is not a whole number, thus, a regular polygon with measure of each interior angle as 22⁰ is not possible.