Question

In triangle PQR and MST, ∠P = 55°, ∠Q = 25°, ∠M = 100° and ∠S = 25°. Is ∆QPR ~ ∆TSM? Why?

Answer 1

We know that, the sum of three angles of a triangle is 180°.

In ∆PQR,

∠P + ∠Q + ∠R = 180°

⇒ 55° + 25° + ∠R = 180°

⇒∠R = 180° – (55° + 25°)

= 180° – 80°

= 100°

In ∆TSM,

∠T + ∠S + ∠M = 180°

⇒ ∠T + ∠25° + 100° = 180°

⇒ ∠T = 180° – (25° + 100°)

= 180° – 125°

= 55°

In ∆PQR and ∆TSM,

∠P = ∠T,

∠Q = ∠S

And ∠R = ∠M

∴ ∠PQR = ∠TSM   ...[Since, all corresponding angles are equal]

Hence, ∆QPR is not similar to ∆TSM, since correct correspondence is P `↔` T, Q `↔` S and R `↔` M.