Question

$\Delta ABC\sim \Delta PQR$, ∠B = 50° and ∠C = 70° . Then ∠P is equal to:

• A. ${50}^{\circ }$
• B. ${60}^{\circ }$
• C. ${40}^{\circ }$
• D. ${70}^{\circ }$

Answer 1

The correct option is B ${60}^{\circ }$

We know that,
Similar triangles have corresponding angles equal.

So,
∠Q = ∠B = ${50}^{\circ }$,
∠R = ∠C = ${70}^{\circ }$ and
∠P = ∠A.

By angle sum property,
∠A + ∠B + ∠C = ${180}^{\circ }$
∠A + ${50}^{\circ }$ + ${70}^{\circ }$ = ${180}^{\circ }$
​​​​​∠A = ${180}^{\circ }$- ${50}^{\circ }$ - ${70}^{\circ }$
∠A = ${60}^{\circ }$

Since, ∠P = ∠A
Hence, ∠P = ${60}^{\circ }$