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