** ****QUESTIONS-:**

*1Find the value of ‘p’ from the following figures*

*Ans.-(a)*

Here, 125° + a = 180° => 180° – 125° = 55° (Linear pair)

125° + b = 180° =>180° – 125° = 55° (Linear pair)

p = a + b (exterior angle of a triangle is equal to the sum of two opposite interior two angles)

=> p = 55° + 55° = 110°

(b)

Two interior angles are right angles = 90°

70° + a = 180° => a = 180° – 70° = 110° (Linear pair)

60° + b = 180° =>b = 180° – 60° = 120° (Linear pair)

The given figure consisting of five sides and it is a pentagon.

Hence, the sum of the angles of a pentagon = 540°

90° + 90° + 110° + 120° + q = 540°

=>410° + y = 540° => q = 540° – 410° = 130°

p + q = 180° (Linear pair)

=> p + 130° = 180°

=> p = 180° – 130° = 50°

*2. Obtain the value for each of the exterior angle of a regular polygon with*

* (i) 10 sides (ii) 25 sides*

* *

** Ans.- **Sum of angles a regular polygon having side a = (a-2)×180°

(i) Sum of angles a regular polygon having side 10 = (10-2)×180°

= 8×180° = 1440°

Each interior angle = 1440°/10 = 144°

Each exterior angle = 180° – 144° = 36°

Or,

Each exterior angle = Sum of exterior angles/Number of sides = 360°/10 = 36°

(i) Sum of angles a regular polygon having side 25 = (25-2)×180°

= 23×180° = 4140°

Each interior angle = 4140°/25 = 165.6°

Each exterior angle = 180° – 165.6° = 14.4°

Or,

Each exterior angle = Sum of exterior angles/Number of sides = 360°/25 = 14.4°

*3. Calculate the number of sides a regular polygon will have if the value of an exterior angle is 36°?*

** Ans.-**As we know that, Each exterior angle = Sum of exterior angles/Number of sides

So, 36° = 360°/Number of sides

=>Number of sides = 360°/36° = 10

Hence therefore, the regular polygon have 15 sides.

*4. A regular polygon having each of its interior angles 144°. Calculate the number of sides it will have.*

** Ans.-**Given, Interior angle = 144°

Exterior angle = 180° – 144° = 36°

Number of sides = Sum of exterior angles/exterior angle

=>Number of sides = 360°/36° = 10

Thus, the regular polygon have 10 sides.

* *

*5. (a) Can a regular polygon have each exterior angle with a measure of 37°?*

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

* *

** Ans.-**(a) Exterior angle = 22°

Number of sides = Sum of exterior angles/exterior angle

=>Number of sides = 360°/37° = 9.72

No, we cannot have a regular polygon with each exterior angle as 37° as it is not divisor of 360.

(b) Interior angle = 37°

Exterior angle = 180° – 37°= 143°

No, we can’t have a regular polygon with each exterior angle as 143° as it is not divisor of 360.

* *

*6. (a) Find the minimum possible interior angle for a regular polygon? Why?
(b) Find the maximum possible exterior angle for a regular polygon?*

* *

** Ans.-**(a)An equilateral triangle is a regular polygon having 3 sides with the least possible minimum interior angle as the regular polygon with minimum sides can be constructed with 3 sides at least..

Since, sum of the interior angles of a triangle = 180°

Each interior angle = 180°/3 = 60°

(b) Equilateral triangle is regular polygon with 3 sides has the maximum exterior angle because the regular polygon consisting least number of sides have the maximum exterior angle possible.

Maximum exterior possible = 180 – 60° = 120°