## ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 13 Understanding Quadrilaterals Ex 13.1

Question 1.

Some figures are given below.

Classify each of them on the basis of the following:

(a) Simple curve

(b) Simple closed curve

(c) Polygon

(d) Convex polygon

(e) Concave polygon

Solution:

Question 2.

How many diagonals does each of the following have?

(a) A convex quadrilateral

(b) A regular hexagon

Solution:

(a) A convex quadrilateral: It has two diagonals.

(b) A regular hexagon: It has 9 diagonals as shown.

Question 3.

Find the sum of measures of all interior angles of a polygon with the number of sides:

(i) 8

(ii) 12

Solution:

Question 4.

Find the number of sides of a regular polygon whose each exterior angles has a measure of

(i) 24°

(ii) 60°

(iii) 72°

Solution:

Question 5.

Find the number of sides of a regular polygon if each of its interior angles is

(i) 90°

(ii) 108°

(iii) 165°

Solution:

Question 6.

Find the number of sides in a polygon if the sum of its interior angles is:

(i) 1260°

(ii) 1980°

(iii) 3420°

Solution:

Question 7.

If the angles of a pentagon are in the ratio 7 : 8 : 11 : 13 : 15, find the angles.

Solution:

Question 8.

The angles of a pentagon are x°, (x – 10)°, (x + 20)°, (2x – 44)° and (2x – 70°) Calculate x.

Solution:

Question 9.

The exterior angles of a pentagon are in ratio 1 : 2 : 3 : 4 : 5. Find all the interior angles of the pentagon.

Solution:

Question 10.

In a quadrilateral ABCD, AB || DC. If ∠A : ∠D = 2:3 and ∠B : ∠C = ∠7 : 8, find the measure of each angle.

Solution:

Question 11.

From the adjoining figure, find

(i) x

(ii) ∠DAB

(iii) ∠ADB

Solution:

Question 12.

Find the angle measure x in the following figures:

Solution:

Question 13.

(i) In the given figure, find x + y + z.

(ii) In the given figure, find x + y + z + w.

Solution:

Question 14.

A heptagon has three equal angles each of 120° and four equal angles. Find the size of equal angles.

Solution:

Question 15.

The ratio between an exterior angle and the interior angle of a regular polygon is 1 : 5. Find

(i) the measure of each exterior angle

(ii) the measure of each interior angle

(iii) the number of sides in the polygon.

Solution:

Question 16.

Each interior angle of a regular polygon is double of its exterior angle. Find the number of sides in the polygon.

Solution: