Question

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

Answer 1

Ratio of angles of the quadrilateral = 3:4:5:6

Let common ratio = x

Then, angles = 3x, 4x, 5x, 6x

According to the question :-

3x+4x+5x+6x = 360°

18x = 360°

x = 360/18

x = 20°

Then,

Angles = 3×20, 4×20, 5×20, 6×20

Then, all the angles of the quadrilateral are 60°, 80°, 100°, 120°.

Answer 2

Firstly consider quadrilateral ABCD

In question the ratio of angles are given so write it as 3x , 4x , 5x and 6x

As we know that some of angles of quadrilateral is 360°

therefore

360° = 3x + 4x + 5x + 6x

360° = 7x + 11x

360° = 18x

360°÷ 18 = x

20° = x

3x = 3 ×20° = 60°

4x = 4 ×20° = 80°

5x = 5 ×20° = 100°

6x = 6× 20° = 120°

The measure of angles is 60° , 80° , 100° and 120°