Question

in the given figure, if angle p is equal to 25 degrees then the measure of angle r is

Answer 1

Answer:

in the given figure if angle p is 25 free then the measure of angle r is

Answer 2

Given:

∠P = 25°

PS = ST = QT = QR

To Find: Value of ∠R.

Calculation:

In ΔPST:

• Since, SP = ST
• So, ∠SPT = ∠STP = 25°
• Also, sum of angles in a triangle is 180°,
• ∠TSP + ∠SPT + ∠STP = 180°
• ∠TSP + 25° + 25° = 180°
• ∠TSP = 130°

From straight line PSQ:

• ∠TSP + ∠TSQ = 180°
• ∠TSQ = 180° - ∠TSP = 180° - 130° = 50°

In ΔTSQ:

• Since TS = TQ
• So, ∠TSQ = ∠TQS = 50°
• ∠TSQ + ∠TQS + ∠STQ = 180°
• 50° + 50° + ∠STQ = 180°
• ∠STQ = 80°

From straight line PR:

• ∠PTS + ∠STQ + ∠RTQ = 180°
• 25° + 80° + ∠RTQ = 180°
• ∠RTQ = 75°
• Since QT = QR
• So ∠QTR = ∠QRT = 75°

Answer:

Value of ∠R is 75°.

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