Question

In Fig., if BP || CQ and AC = BC, then the measure of x is

A. 20°

B. 25°

C. 30°

D. 35°

Answer 1

Given,

BP ‖ CQ

And,

AC ‖ BC

∠A = ∠ABC (Since, AC = BC)

In ΔABC

∠A + ∠B + ∠C = 180°

∠A + ∠A + ∠C = 180°

2∠A + ∠C = 180°(i)

∠ACB + ∠ACQ + ∠QCD = 180°(Linear pair)

∠ACB + x = 110°(ii)

∠PBC + ∠BCQ = 180°(Co. interior angle)

20° + ∠A + ∠ACB + x = 180°

∠A = 50°(iii)

Using (iii) in (i), we get

2 x 50° + ∠ACB = 180°

∠ACB = 80°

Using value of ∠ACB in (ii) l we get

80° + x = 110°

x = 30°