Question

In a triangle PQR and MST, ∟P=55°, ∟Q = 25°, ∟M = 100° and ∟S = 25°. Is ΔQPR similar to ΔTSM? Why?

Answer 1

Answer:

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

In ΔPQR, ∠P + ∠Q + ∠R = 180°

⇒ 55° + 25° + ∠R = 180°

⇒ ∠R = 180° – (55° + 25°)= 180° – 80° =100°

In ΔTSM, ∠T + ∠S + ∠M = 180°

⇒ ∠T + ∠25°+ 100° = 180°

⇒ ∠T = 180°-(25° +100°)

=180°-125°= 55°

In ΔPQR and A TSM, and

∠P = ∠T, ∠Q = ∠S,

and ∠R = ∠M

ΔPQR ~ ΔTSM [since, all corresponding angles are equal]

Hence, ΔQPR is not similar to ΔTSM, since correct correspondence is P ↔ T, Q < r→ S and R ↔M

Step-by-step explanation:

hope it will help you.....