Question

in the figure given below find the value of aob,aof,eof,doe
​

Answer 1

Answer:

∠AOB = 60°

∠AOF = 20°

∠EOF = 120°

∠DOE = 40°

Step-by-step explanation:

First to find x

As DOA = 180°

90° + 30° + x = 180°

120° + x = 180°

x = 180° - 120°

x = 60°

Then, to find y

As DOA = 180°

$y + \frac{x}{3} +2x = 180$

Substitute x with 60°

$y +\frac{60}{3} + (2*60) = 180\\y+20+120=180\\y + 140 = 180\\y = 180 - 140\\y = 40$

∠AOB = x = 60°

∠AOF = x/3 = 60/3 = 20°

∠EOF = 2x = 2*60 = 120°

∠DOE = y = 40°

Verification:

90° + 30° + x + x/3 + 2x + y = 360°

120° + 60° + 60°/3 + (2*60)° + 40° = 360°

180° + 20° + 120° + 40° = 360°

360° = 360°