# In ∆PQR and ∆MST, ∠P = 55°, ∠Q = 25°, ∠M = 100° and ∠S = 25°. Is ∆QPR ∼ ∆TSM? Why? (True)

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°

Similarly, in ∆TSM,

T + S + M = 180°

T + 25° + 100° = 180°

⇒ ∠T = 180°- (25° + 100°)

T = 180° - 125° = 55°

In ∆PQR and ∆TSM,

P = T,

Q = S

And

R = M

So, ∆PQR TSM

Since, all corresponding angles are equal

Hence,

∆QPR is similar to ∆TSM,

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