Question

In Fig. find the values of x and y and then shows that AB||CD.

(i) ∠x = ? 

(ii) ∠y = ? 

(iii) Show that AB||CD.

Answer 1

(i) PQ Bisects AB at R. 

∠PRA and ∠ARS are on straight line PQ. 

∴ ∠PRA + ∠ARS = 180° 

Adjacent angles 

50 + ∠ARS = 180° 

∠ARS = 180 – 50 

∴ x = ∠ARS = 130° (i)

(ii) Similarly, PQ straight line intersects straight line CD at S. 

∴∠CSQ = ∠RSD . 

Vertically opposite angles 

∴y = ∠RSD = 130° (ii) From (i) and (ii), 

∠ARS = ∠RYD 

x = y = 130°

(iii) These are mutual alternate angles 

∴x = y = 130° 

∴ AB || CD.