Question

In the given figure, if the exterior angle is 135degree then angleP is​

Answer 1

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Answer 2

Answer:

90°.

Step-by-step explanation:

Given:- PQ=PR and exterior angle=135°.

To prove:- Angle QPR.

Proof:- 1)PQ=PR (Given).

2)Angle R= Angle Q ( Angles opposite to equal sides are equal).

Let Angle PRQ be= X.

Angle PRQ= Angle PQR .

Which is equal to X.

Angle PRQ+ Angle 135°=180°. (Linear pair)

Angle X + Angle 135°= 180°.

Angle X= 180°- Angle 135°.

Angle X= 45°.

Hence, the value of X= 45° and Angle PRQ= Angle PQR=45°

Angle PQR+ Angle QRP+ Angle RPQ=180°.

( Angel sum property of triangle).

45°+45°+ Angle QPR= 180°.

90°+ Angle QPR= 180°.

Angle QPR= 180°-90°.

Angle QPR= 90°.

Hence, the angle P is 90°.

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