CBSE2026Class Class 10 · Mathematics1 Marks · Mcq✅ Verified
From the figures given below, which of the following is true about the measure of $\angle P$ ?
In $\triangle ABC$: $AB=3.8$ cm, $BC=6$ cm, $AC=3\sqrt{3}$ cm, $\angle A=80^{\circ}$, $\angle B=60^{\circ}$.
In $\triangle PQR$: $PQ=12$ cm, $QR=7.6$ cm, $PR=6\sqrt{3}$ cm.
A. $\angle P=60^{\circ}$
B. $\angle P=80^{\circ}$
C. $\angle P=40^{\circ}$
D. The measure of $\angle P$ cannot be determined
✅ Answer & Solution
✅ Correct Answer: A
Step 1: Compare the ratios of the sides of the two triangles.
$$\frac{PQ}{BC}=\frac{12}{6}=2,\qquad \frac{QR}{AB}=\frac{7.6}{3.8}=2,\qquad \frac{PR}{CA}=\frac{6\sqrt{3}}{3\sqrt{3}}=2$$
Step 2: All three ratios are equal, so by SSS similarity criterion the triangles are similar with the correspondence
$$\triangle PQR \sim \triangle BCA$$
Step 3: In similar triangles, corresponding angles are equal. Here $P \leftrightarrow B$.
$$\angle P=\angle B=60^{\circ}$$
Correct option is (A) $\angle P=60^{\circ}$.
