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