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

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

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

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.

In Fig. 8.45, OP, OQ, OR and OS are four rays, prove that:

∠POQ + ∠QOR + ∠SOR + ∠POS = 360°