Question

$\Delta PQR=\Delta ABC$ if $PQ=5cm.\angle Q={40}^0$ and $\angle P={80}^0$ then which of the following are true?

• A. $AB=5cm,\angle A={60}^0$
• B. $AB=5cm,\angle C={60}^0$
• C. $BC=5cm,\angle C={60}^0$
• D. $BC=5cm,\angle B={40}^0$

Answer 1

Answer: (B)

In $△PQR$ using angle sum property of triangle

$\angle P+\angle Q+\angle R={180}^{\circ }{80}^{\circ }+{40}^{\circ }+\angle R={180}^{\circ }\Rightarrow \angle R={180}^{\circ }-{120}^{\circ }={60}^{\circ }$

Now $△PQR\cong △ABC$

As corresponding parts of congruent triangle are equal

$\therefore AB=PQ=5cm$ and $\angle C={60}^{\circ }$