In ΔPQR, S and T are mid-points of PQ and PR, respectively. If ∠QPR = 75° and ∠PRQ = 40°, then ∠TSQ is :

115°

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°