three angles of a qadrilateral are in the ratio 2:3:7 .the mean of these angles is 64 .find all the angles

Answer 1

Angles :

A , B , C and D

( A + B + C ) / 3 = 64 Multiply both sides by 3

A + B + C = 3 * 64 = 192 °

A / B = 2 / 3 Multiply both sides by 3

3 A / B = 2 Multiply both sides by B

3 A = 2 B Divide both sides by 3

A = 2 B / 3

B / C = 3 / 7 Multiply both sides by 7

7 B / C = 3 Multiply both sides by C

7 B = 3 C Divide both sides by 3

7 B / 3 = C

C = 7 B / 3

A + B + C = 2 B / 3 + B + 7 B / 3 = 192 °

2 B / 3 + 3 B / 3 + 7 B / 3 = 192 °

12 B / 3 = 192 ° Multiply both sides by 3

12 B = 3 * 192 °

12 B = 576 ° Divide both sides by 12

B = 576 ° / 12

B = 48 °

A = 2 B / 3

A = 2 * 48 / 3 = 96 / 3 = 32 °

C = 7 B / 3

C = 7 * 48 / 3 = 336 / 3 = 112 °

D = 360 ° - ( A + B + C )

D = 360 ° - 192 °

D = 168 °