Question

22. In Fig. 11.51, if BP || CQ and AC = BC, then the measure of x is​

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°

Answer 2

Answer:

Step-by-step explanation: 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°