Q13 of 115 Page 8

In Fig. 8.42, a is greater than b by one third of a right angle. Find the values of a and b.

a +b = 180^o (Linear pair)

a =180^o - b (i)

Now, given that

a = b + * 90^o

a = b + 30^o (ii)

a – b = 30^o

Equating (i) and (ii), we get

180^o – b = b + 30^o

150^o = 2b

b = 75^o

Hence, a = 180^o – b

= 105^o

In Fig. 8.40, ∠ACB is a line such that ∠DCA = 5x and ∠DCB = 4x. Find the value of x.

Given ∠POR = 3x and ∠QOR = 2x+10, find the value of x for which POQ will be a line.

What value of y would make AOB a line in Fig. 8.43, if ∠AOC= 4y and ∠BOC =(6y+30)

In Fig. 8.44, ∠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.