Question

The angles of a quadrilateral are in the ratio of 9 : 8 : 7 : 6. Find all the angles of the quadrilateral.​

Answer 1

Answer:

108°,96°,84°,72°.

l hope this helps you.

Answer 2

Given:-

• All angles of quadrilateral are in ratio of 9:8:7:6.

To find:-

• All angles of quadrilateral.

Solution:-

Let the First angle of quadrilateral be 9x°.

Second angle of quadrilateral be 8x°.

Third angle of quadrilateral be 7x°.

Fourth angle of quadrilateral be 6x°.

We know that,

Sum of all interior angles of quadrilateral is 360°.

So,

$\implies \sf 9x \degree + 8x \degree + 7x \degree + 6x \degree = 360 \degree$

$\implies \sf 30x \degree = 360 \degree$

$\implies \sf \: x = \dfrac{360 \degree}{30}$

$\implies \boxed{ \sf x = 12 \degree}$

Verification:-

$\implies \sf 9x \degree + 8x \degree + 7x \degree + 6x \degree = 360 \degree$

• Put x = 12°.

$\implies \sf (9 \times 12) \degree + (8 \times 12) \degree + (7 \times 12) \degree + (6 + 12) \degree = 360 \degree$

$\implies \sf 108 \degree + 96 \degree + 84 \degree + 72 \degree = 360 \degree$

$\implies \sf 360\degree = 360 \degree$

Hence, Verified.

Therefore,

First angle of quadrilateral = 9×12 = 108°.

Second angle of quadrilateral = 8×12 = 96°.

Third angle of quadrilateral = 7×12 = 84°.

Fourth angle of quadrilateral = 6×12 = 72°.