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Understanding Quadrilaterals

    Execise 3.2

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8th class > Understanding Quadrilaterals > Execise 3.2

Execise 3.2

1. Find x in the following figures:

(a)

Solution:

Three exterior angles 125°, 125° and x.

We know that, sum of the exterior angles = °

Thus, 125° + 125° + x = 360°

° + x = 360°

x = °

(b)

Solution: Our exterior angles are : x ,90°, 60°, 90°, 70°.

We know that:

Sum of exterior angles = 360°

x + 90° + 60° + 90° + 70° = 360°

x = 360° - ° = °

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

(i) 9 sides

(ii) 15 sides

Solution:

(i) Exterior angle = 360°n where n = Number of sides (for regular polygon).

Given: no. of sides of regular Polygon =

Exterior angle = 360°9 = °

(ii) Exterior angle = 360°n where n = Number of sides (regular polygon).

Given: Number of sides of regular Polygon =

Exterior angle = 360°15 = °

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

Solution:

Exterior angle is 24°

In a regular polygon, sum of the exterior angles = 360°

Exterior Angle x Number of sides = 360°

° x n = °

n = 360°24° =

Thus, the regular polygon has a total of 15 sides.

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

Solution:

By linear Pair: Interior Angle + Exterior Angle = 180°

° + Exterior Angle = °

Exterior Angle = °

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?

Solution:

(a) In a regular polygon, sum of the exterior angles = 360°

° x n = °

n =

But n be in decimal.

Thus, a 22° external angle measure is not possible.

(b) By linear pair: Interior Angle + Exterior Angle = 180°.

° + External Angle = °

External Angle = °

In a regular polygon, sum of the exterior angles = 360°

158° x n = 360°

n = 360°158° =

Since n cannot be in decimals, 158° external angle measure is not possible.

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?

(a) Consider a regular polygon having the least number of sides:

We know that the sum of all the angles of a triangle = °

x + x + x = 180°

x = 180°

x = °

The minimum interior angle possible for a regular polygon is 60°.

(b)

Consider the interior angle to be 60° since an equilateral triangle is a regular polygon having maximum exterior angle because it consists of the least number of sides.

Exterior angle = 180° - ° = °

The maximum exterior angle possible for a regular polygon is 120°.