Question 39

The side QR of ΔPQR is produced to S. If ∠PRS = 105° and ∠Q = (1/2)∠P, then what is the value of ∠P?

Solution

Let $$\angle Q=x$$, => $$\angle P=2x$$

Using exterior angle property in $$\triangle$$ PQR,

=> $$\angle$$ P + $$\angle$$ Q = $$\angle$$ PRS

=> $$2x+x=105^\circ$$

=> $$x=\frac{105^\circ}{3}=35^\circ$$

$$\therefore$$ $$\angle P=2\times35^\circ=70^\circ$$

=> Ans - (C)

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