Question

In the figure find the value of x

Answer 1

Exterior angle is equal to the sum of opposite interior angles.

In ∆TSP ∠TSP + ∠SPT = ∠UTP

75° + ∠SPT = 105°

∠SPT = 105° – 75°

∠SPT = 30°  ...(1)

∠SPT + ∠TPR + ∠RPQ = 180°  ...[∵ Sum of angles at a point on a line is 180°]

30° + 90° + ∠RPQ = 180°

120° + ∠RPQ = 180°

∠RPQ = 180° – 120°

∠RPQ = 60°  ...(2)

∠VRQ + ∠QRP = 180°   ...[∵ linear pair]

145° + ∠QRP = 180°

∠QRP = 180° – 145°

∠QRP = 35°

Now in ∆PQR

∠QRP + ∠RPQ = x  ...[∵ x in the exterior angle]

35° + 60° = x

95° = x