In ΔPQR, S and T are mid-points of PQ and PR, respectively. If ∠QPR = 75° and ∠PRQ = 40°, then ∠TSQ is :
Answer & explanation
Correct answer: option 4
We have,
∠QPR = 75°
∠PRQ = 40°
We know that,
Sum of all three angles of a triangle = 180°.
In ΔPQR
= ∠QPR + ∠PQR + ∠PRQ = 180°
= 75° + ∠PQR + 40° = 180°
= ∠PQR = 180° - 115°
= ∠PQR = 65°
Also, ΔPQR ~ ΔPST
∠PST = ∠PQR = 65°
Now,
∠PST + ∠TSQ = 180°
= 65° + ∠TSQ = 180°
= ∠TSQ = 180° - 65°
∠TSQ = 115°