Question

In Fig., ∠AOF and ∠FOG form a linear pair.

∠EOB = ∠FOC = 90° and ∠DOC = ∠FOG = ∠AOB = 30°

(i) Find the measures of ∠FOE, ∠COB and ∠DOE.

(ii) Name all the right angles.

(iii) Name three pairs of adjacent complementary angles.

(iv) Name three pairs of adjacent supplementary angles.

(v) Name three pairs of adjacent angles.

Answer 1

(i) Say,

∠FOE = x

∠DOE = y

∠BOC = z

∠AOF + 30° = 180°(∠AOF + ∠FOG = 180°)

∠AOF = 150°

∠AOB + ∠BOC + ∠COD + ∠DOE + ∠EOF = 150°

30° + z + 30° + y + x = 150°

x + y + z = 90°(i)

Now,

∠FOC = 90°

∠FOE + ∠EOD + ∠DOC = 90°

x + y + 30° = 90°

x + y = 60°(ii)

Using (ii) in (i), we get

x + y + z = 90°

60° + z = 90°

z = 30°(∠BOC = 30°)

∠BOE = 90°

∠BOC + ∠COD + ∠DOE = 90°

30° + 30° + ∠DOE = 90°

∠DOE = 30°

Now, we have

x + y = 60°

y = 30°

∠FOE = 30°

(ii) Right angles are:

∠DOG, ∠COF, ∠BOF, ∠AOD

(iii) Three pairs of adjacent complimentary angles are:

∠AOB, ∠BOD

∠AOC, ∠COD

∠BOC, ∠COE

(iv) Three pairs of adjacent supplementary angles are:

∠AOB, ∠BOG

∠AOC, ∠COG

∠AOD, ∠DOG

(v) Three pairs of adjacent angles are:

∠BOC, ∠COD

∠COD, ∠DOE

∠DOE, ∠EOF