Question

The angles of a quadrilateral are in the ratio 1: 2: 7:8 .Find angles of the quadrilateral. What type of quadrilateral is it ​

Answer 1

Given :

• The angles of a quadrilateral is in the ratio of 1:2:7:8

To find :

• Angles of the quadrilateral

According to the question,

Let the angles be 1x,2x,7x and 8x

As we know,

Sum of all angles of a quadrilateral is 360°

→ 1x + 2x + 7x + 8x = 360°

→ 18x = 360°

→ x = 360° ÷ 18

.°. x = 20°

★ Value of 1x :

→ 1x

→ 1(20°)

→ 20°

★ Value of 2x :

→ 2x

→ 2(20°)

→ 40°

★ Value of 7x :

→ 7x

→ 7(20°)

→ 140°

★ Value of 8x :

→ 8x

→ 8(20°)

→ 160°

As we can see that all angles are different so the quadrilateral is trapezium..

Answer 2

Ratio of the angles = 1:2:7:8

Let the common among the angles be = k

We know, sum of interior angles of a quadrilateral = 360°

A.T.Q.:-

∴ x + 2x + 7x + 8x = 360°

⇒ 18x = 360°

⇒ x = 20°

∴ The angles are 20°, 40°, 140°, and 160°. [Put the value of (x) in the variable angles.]