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# Question and Answer

In the figure side $$QR$$ of a $$\Delta PQR$$ has been produced to the point $$S$$. If $$\angle PRS=115^{\circ }$$ and $$\angle P=45^{\circ }$$ , then $$\angle Q$$ is equal to
（ ）
A. $$70^{\circ }$$
B. $$105^{\circ }$$
C. $$51^{\circ }$$
D. $$80^{\circ }$$
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## QuestionMathsClass 7

In the figure side $$QR$$ of a $$\Delta PQR$$ has been produced to the point $$S$$. If $$\angle PRS=115^{\circ }$$ and $$\angle P=45^{\circ }$$ , then $$\angle Q$$ is equal to
（ ）
A. $$70^{\circ }$$
B. $$105^{\circ }$$
C. $$51^{\circ }$$
D. $$80^{\circ }$$

A
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## Solution

Since$$\angle PRS+\angle PRQ=180^{\circ}$$[Linear pair]
$$\implies 115^{\circ}+\angle PRQ=180^{\circ}$$
$$\implies \angle PRQ=180^{\circ}-115^{\circ}$$
$$\implies \angle PRQ=65^{\circ}$$
In $$\triangle PQR$$,
$$\angle PRQ+\angle RPQ+\angle PQR=180^{\circ}$$[As the sum of interior angles of a triangle is $$180^{\circ}$$ ]
$$\implies \angle PQR=180^{\circ}-65^{\circ}-45^{\circ}$$
$$\implies \angle PQR=70^{\circ}$$
So, $$\angle Q=70 ^{\circ}$$
Thus, option (A) is correct.