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Question
In the figure find the value of x
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Solution
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
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