## Chapter 3 Understanding Quadrilaterals Exercise 3.2

**Question 1: Find x in the following figures.**

**Answer:**

a)

= 125° + 125° + x° = 360° (sum of exterior angles = 360°)

= 250° + x = 360°

= x = 360 - 250

= x = 70°

b)

= 70° + x° + 90° + 60° + 90° = 360° (sum of exterior angles = 360°)

= 310° + x = 360°

= x = 360 - 310

= x = 50°

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

(i) 9 sides

(ii) 15 sides

Answer:

(i) 9 sides

(ii) 15 sides

Answer:

a)

Number of sides = 9

Measure of exterior angle = ?

Formula = 360°/number of sides

Solution

= 360°/9

= 40°

b)

Number of sides = 15

Measure of exterior angle = ?

Formula = 360°/number of sides

Solution

= 360°/15

= 24°

**Question 3: How many sides does a regular polygon have if the measure of an exterior angle is 24°?**

Answer:

Answer:

Measure of exterior angle = 24°

Number of sides = ?

Formula = 360°/measure of exterior angle = number of sides

Solution

= 360°/24

= 15 sides

Therefore, the regular polygon has 15 sides.

**Question 4: How many sides does a regular polygon have if each of its interior angles is 165°?**

Answer:

Answer:

Measure of interior angle = 165°

Measure of exterior angle = ?

= 180° - 165° = 15° (supplementary angles equal to 180°)

Therefore, the measure of exterior angle is 15°.

Measure of exterior angle = 15°

Number of sides = ?

Formula = 360°/measure of exterior angle = number of sides

Solution

= 360°/15

= 24 sides

Therefore, the regular polygon has 15 sides.

**Question 5:**

a) Is it possible to have a regular polygon with measure of each exterior angle as 22°?

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

Answer:

a) Is it possible to have a regular polygon with measure of each exterior angle as 22°?

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

Answer:

a) The sum of all the exterior angles of a regular polygon is equal to 360° which is not divisible by 22°. Therefore, it is not possible to have a regular polygon with exterior angle as 22°.

b) No, it can be an interior angle of a regular polygon as each exterior angle is 180° - 22° = 158°, which is not a divisor of 360°.

**Question 6:**

a) What is the minimum interior angle possible for a regular polygon? Why?

b) What is the maximum exterior angle possible for a regular polygon?

Answer:

a) What is the minimum interior angle possible for a regular polygon? Why?

b) What is the maximum exterior angle possible for a regular polygon?

Answer:

a) Equilateral triangle is a regular polygon with 3 sides that has the minimum interior angle as it has the least measure of an interior angle i.e. 60°.

b) Equilateral triangle is a regular polygon with 3 sides has the maximum exterior angle as 180 - 60° = 120° (the regular polygon with least number of sides have the maximum exterior angle possible).

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