Question

In the adjacent figure AB // CD. Find ‘ the values of x, y and z.

Answer 1

Given that AB//CD 

From the adj. fig. ∠AEP + ∠PED + ∠BEC 

= 180° (∵ straight angle)

⇒ x° + 64° + x° = 180° 

⇒ 2x = 180° – 64° = 116°

x = 116°/2 = 58°

Now ∠z + ∠x = 180° [ ∵ AB//CD Zx, Zz are interior angles which are formed same side of the transversal line] 

⇒∠z + 58° = 180° 

⇒ ∠z = 180° – 58° 

∴ ∠z = 122°. 

from ΔAPE 

∠A + ∠P + ∠E = 180° 

⇒ 90° + ∠y + ∠x = 180° 

⇒ 90° + ∠y + 58° = 180° 

⇒ ∠y = 180° – 148° 

⇒ ∠y = 32° 

⇒ ∠x = 58°, ∠y = 32°, ∠z = 122°.