The angles of a quadrilateral are in the ratio 1 : 2 : 3 : 4.

Question:

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

(a) 72o 

(b) 144o 

(c) 36o 

(d) 18o

Solution:

(c) 36o

We know that, sum of all interior angle of quadrilaterals is equal to 360o.

Let us assume the angles be x, 2x, 3x, and 4x

Then,

x + 2x + 3x + 4x = 360o

10x = 360o

x = 360/10

x = 36

Therefore the angles are x = 36o

2x = 2 × 36 = 72o

3x = 3 × 36 = 108o

4x = 4 × 36 = 144o

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