Question

In the figure the line passing through P is parallel to QR. Find x​

Answer 1

Answer:

Value of x is 100°

Step-by-step explanation:

• Line P parallel to line QR

• so by alternate angle theorem

• angle APQ = angle PQR

• so angle PQR = 65 °

• Now line PQ and line PR are similar

• By isoceles Triangle theorem

• angle PQR = angle PRQ

• now angle PRQ = 65 °

• but

• angle PRQ= angle PRT

• angle PRQ = 65 °+ angle TRQ

• 65 ° = 25° + angle TRQ

• angle TRQ = 40°

• now line TQ and line TR are similar

• so angle TQR = angle TRQ
• angle TQR = 40 °

• now in Traingle TQR

• angle TQR + angle TRQ + angle QTR = 180 °

• 40° + 40° + angle QTR = 180°

• angle QTR = 100 °