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The angles of a quadrilateral are in the ratio 1 : 2 : 3 : 4. The smallest angle is
(a) 72°
(b) 144°
(c) 36°
(d) 18°

Solution:

Given, the angles of a quadrilateral are in the ratio 1 : 2 : 3 : 4

We have to find the smallest angle.

Let the angels be x, 2x, 3x and 4x.

We know that the sum of the angles of a quadrilateral is equal to 360 degrees.

So, x + 2x + 3x + 4x = 360°

3x + 7x = 360°

10x = 360°

x = 360°/10

x = 36°

Now, 2x = 2(36°) = 72°

3x = 3(36°) = 108°

4x = 4(36°) = 144°

Therefore, the smallest angle is 36°

✦ Try This: The angles of a quadrilateral are in the ratio 2 : 3 : 3 : 1. The smallest angle is (a) 80°, (b) 144°, (c) 36°, (d) 18°

☛ Also Check: NCERT Solutions for Class 8 Maths

NCERT Exemplar Class 8 Maths Chapter 5 Problem 26

Summary:

The angles of a quadrilateral are in the ratio 1 : 2 : 3 : 4. The smallest angle is 36°

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