Question

2. There are sixcangles at apoint one of
them is 45 and the other five angles are
all equal. What is the measure of all the
five angles ​

Answer 1

Since ∠COE and ∠DOF are vertically opposite angles, we have,

∠COE = ∠DOF

⇒ ∠z = 50o

Also ∠BOD and ∠COA are vertically opposite angles.

So, ∠BOD = ∠COA

⇒ ∠t = 90o

As ∠COA and ∠AOD form a linear pair,

∠COA + ∠AOD = 180o

⇒ ∠COA + ∠AOF + ∠FOD = 180o [∠t = 90o]

⇒ t + x + 50o = 180o

⇒ 90o + xo + 50o = 180o

⇒ x + 140 = 180

⇒ x = 180 – 140 = 40

Since ∠EOB and ∠AOF are vertically opposite angles

So, ∠EOB = ∠AOF

⇒ y = x = 40

Thus, x = 40 = y = 40, z = 50 and t = 90