Question

In the above fig, If $\angle B={50}^{\circ }$ and $\angle R={60}^{\circ }$, then find $\angle C$.

• A. 70${}^{\circ }$
• B. 60${}^{\circ }$
• C. 50${}^{\circ }$
• D. 30${}^{\circ }$

Answer 1

The correct option is A 70${}^{\circ }$

In $△ABC$ and $△QPR$,
AB = QP (given in figure)
BC = PR (given in figure)
CA = RQ (given in figure)

Thus, by SSS criterion for congruency of triangles, $△ABC\cong △QPR$

In $△ABC$,
$\angle A=\angle R={60}^{\circ }$ ..... (corresponding parts of congruent triangles)
$\angle B={50}^{\circ }$ ..... (given)

$\angle A+\angle B+\angle C={180}^{\circ }$ .... (Angle sum property of a triangle)
$\angle C={180}^{\circ }-(\angle A+\angle B)$
$⟹\angle C={180}^{\circ }-({60}^{\circ }+{50}^{\circ }$)
$⟹$ $\angle C={180}^{\circ }-{110}^{\circ }$
$⟹\angle C={70}^{\circ }$