Question

In the given figure, AB || CD and EF || GH. Find the values of x,y, z and t.

Answer 1

In the given figure,
x=60° (Vertically-opposite angles)
∠PRQ=∠SQR (Alternate Angles)

y=60°

∠APR=∠PQS (corresponding Angles) ⇒110°=∠PQR+60° (∵∠PQS=∠PQR+∠RQS)
⇒∠PQR=50°
∠PQR+∠RQS+∠BQS=180° (Since AB is a straight line)

⇒50°+60°+z=180°⇒110°+z=180°⇒z=70°
∠DSH=z (Corresponding Angles)

⇒∠DSH=70° (∴∠DSH=t) Vertically Opposite Angles

⇒t=70°∴ x=60°, y=60°, z=70° and t=70°.