Question

The angles of a quadrilateral are in the ratio 2:3:7:8. Find measures of each angles.

Answer 1

Sum of all the angles of a quadrilateral is 360°.

According to the question,

2x + 3x + 7x + 8x = 360°

=> 20x = 360°

=> x = 360° ÷ 20

=> x = 18°

Hence the measures of the angles are -

2x = 2 × 18° = 36°

3x = 3 × 18° = 54°

7x = 7 × 18° = 126°

8x = 8 × 18° = 144°

The angles of the quadrilateral are 36°, 54°, 126°, and 144°.

Answer 2

Let the four angles of quadrilateral be 2x,

3x, 7x and 8x.

$sum \: of \: all \: angles \: of \: a \\ \: quadrilatetal = {360}^{0}$

$= > 2x + 3x + 7x + 8x = {360}^{0}$

$= > 20x = {360}^{0}$

$= > x = \frac{360}{20}$

$= > x = 18$

So x equals to 18.

First angle=2x =36

Second angle=3x =54

Third angle=7x =126

Fourth angle=8x =144