Question

If angle P=25 degree, find angle R
please answer ​

Answer 1

30° .

Solution :-

In ∆PST ,

→ ∠P = 25° (given)

→ PS = ST (given)

So,

→ ∠SPT = ∠PTS = 25° { Angle opposite to equal sides are equal in measure . }

now, in ∆STQ ,

→ ∠QST = ∠SPT + ∠PTS { Exterior angle is equal to sum of opposite interior angles .}

→ ∠QST = 25° + 25° = 50°

So,

→ ∠QST = ∠SQT { since ST = QT . }

then,

→ ∠QST + ∠SQT + ∠STQ = 180° { By angle sum property }

→ 50° + 50° + ∠STQ = 180°

→ 100° + ∠STQ = 180°

→ ∠STQ = 180° - 100°

→ ∠STQ = 80°

Now, Since P - T - R is a straight line .

→ ∠PTS + ∠STQ + ∠QTR = 180°

→ 25° + 80° + ∠QTR = 180°

→ 105° + ∠QTR = 180°

→ ∠QTR = 180° - 105°

→ ∠QTR = 75°

now, in ∆QTR,

→ ∠QTR = ∠TRQ { since QT = QR }

therefore,

→ ∠R = 75° (Ans.)

Hence , ∠R is equal to 75° .

Learn more :-

In the figure along side, BP and CP are the angular bisectors of the exterior angles BCD and CBE of triangle ABC. Prove ∠BOC = 90° - (1/2)∠A .

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