Question

In the adjoining figure, three coplanar lines AB, CD and EF intersect at a point O, forming angles as shown. Find the values of x, y, z and t.

Answer 1

From the figure we know that ∠COE and ∠DOF are vertically opposite angles

∠COE = ∠DOF = ∠z = 50^o

From the figure we know that ∠BOD and ∠COA are vertically opposite angles

∠BOD = ∠COA = ∠t = 90^o

We also know that ∠COA and ∠AOD form a linear pair

∠COA + ∠AOD = 180^o

It can also be written as

∠COA + ∠AOF + ∠FOD = 180^o

By substituting values in the above equation we get

90^o + x^o + 50^o = 180^o

On further calculation we get

x^o + 140^o = 180^o

x^o = 180^o – 140^o

By subtraction

x^o = 40^o

From the figure we know that ∠EOB and ∠AOF are vertically opposite angles

∠EOB = ∠AOF = x = y = 40

Therefore, the values of x, y, z and t are 40, 40, 50 and 90.