# Understanding Quadrilaterals – Chapter 3

**CBSE CLASS 8 MATHEMATICS**

**Understanding Quadrilaterals – Chapter 3**

**Extra Questions For Practice**

1. State the name of a regular polygon of

a) 3 sides

b) 4 sides

c) 5 sides

2. In a quadrilateral the three angles are given as 110, 50 and 140 degrees. What will be the measure of the fourth angle?

3. Find the number of sides of a regular polygon whose each exterior angle has a measure of 60 degree.

4. Find the measure of each exterior angle of a regular polygon of

a) 6 sides

b) 12 sides

5. How many sides does a regular polygon have if the measure of an exterior angle is 30 degrees?

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

7. Find the perimeter of a parallelogram whose sides are 24 cm and 10 cm.

8. In a quadrilateral, the measures of three angles are equal and fourth angle is 120 degrees. Find the other angles.

9. The angles of a quadrilateral are in the ratio 3:4:5:6. Find the measure of each angle.

10. Find the measure of an interior angle of a regular polygon of 6 sides.

**ANSWERS:**

1. a) Equilateral Triangle

b) Square

c) Regular Pentagon

2. We know that the sum of the measures of the four angles of a quadrilateral is 360 degrees.

Given the three angles are 110, 50 and 140 degrees.

Then fourth angle = 360 – (110 + 50 + 140) = 360 – 300 = 60 degrees.

3. Total measure of all exterior angles = 360

Measure of each exterior angle = 60

Therefore, the number of exterior angles = 360/60 = 6

The polygon has 6 sides.

4. a) We know that the sum of all the exterior angles of a polygon = 360

Measure of each angle of 6 sided regular polygon = 360/6 = 60 degrees.

b) Measure of each angle of 12 sided regular polygon = 360/12 = 30 degrees.

5. The sum of all the exterior angles of a polygon = 360 degrees.

Number of sides = 360 / Measure of an angle = 360 /30 = 12 sides.

6. Sum of all interior angles = (n-2) x 180

Measure of each angle = (n-2) x 180/n

Therefore, (n-2) x 180/n = 165

(n-2) x 180 = 165n

180n – 360 = 165n

180n – 165n = 360

15n = 360

n = 360/15 = 24.

7. In a parallelogram opposite sides are equal.

Given sides are 24 cm and 10 cm.

Therefore, perimeter = 24 + 24 + 10 + 10 = 68 cm

8. Let the measure of the three equal angles be x.

Given fourth angle is 120 degrees.

We know that sum of the four angles = 360 degrees.

Therefore, x + x + x + 120 = 360

3x + 120 = 360

3x = 360 – 120 = 240

x = 240/3 = 80 degrees.

9. Given ratio is 3:4:5:6.

Sum of the parts = 3+4+5+6 = 18

The measure of first angle = 360 x 3/18 = 60

The measure of second angle = 360 x 4/18 = 80

The measure of third angle = 360 x 5/18 = 100

The measure o fourth angle = 360 x 6/18 = 120.

10. Measure of an interior angle of a regular polygon of n sides = (n-2) 180/n

So measure of an interior angle of a regular polygon of 6 sides = (6-2) 180/6

= 4 x 180/6 = 120 degrees.