NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 6: Triangles - Exercise 6.2

Question 5

Step 1: Find the missing angle in triangle PQR.

We know the sum of angles in any triangle is \(180^\circ\).

In \(\triangle PQR\):

\(\angle R = 180^\circ - (\angle P + \angle Q)\)

\(= 180^\circ - (55^\circ + 25^\circ)\)

\(= 180^\circ - 80^\circ = 100^\circ\).

So the three angles of \(\triangle PQR\) are: 55°, 25°, and 100°.

Step 2: Find the missing angle in triangle MST.

In \(\triangle MST\):

\(\angle T = 180^\circ - (\angle M + \angle S)\)

\(= 180^\circ - (100^\circ + 25^\circ)\)

\(= 180^\circ - 125^\circ = 55^\circ\).

So the three angles of \(\triangle MST\) are: 100°, 25°, and 55°.

Step 3: Match the equal angles of both triangles.

• \(\angle Q = 25^\circ \leftrightarrow \angle S = 25^\circ\)
• \(\angle P = 55^\circ \leftrightarrow \angle T = 55^\circ\)
• \(\angle R = 100^\circ \leftrightarrow \angle M = 100^\circ\)

Step 4: Write the correct order of similarity.

Corresponding equal angles must come in the same order.

So the correct similarity is: \(\triangle QPR \sim \triangle STM\).

Not \(\triangle TSM\).