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.