Question

in the given figure PQ, PR and ST, are tangents to the same circle. if angle P is equal to 40 degree and Angle qrt is equal to 75 find a ,b and c.​

Answer 1

Here you go!

All the best for math exam tomorrow, I'm writing it too!

Answer 2

Given,

In the given figure PQ, PR and ST, are tangents to the same circle. ∠P = 40° and ∠QRT = 75°

To Find,

∠a, ∠b and ∠c

Solution,

PQ = PR (tangents)

∴ 40° + a + a = 180°

  2a = 180 - 40

     ∠a = 70°

Joining QT, we get

∠QRT = ∠RQA = 75°

(Angle mad by chord and tangent = Angle in opposite segment)

In ΔQRT,

∠TQR = 180 - (70 + 75) = 180 - 145 = 35°

∠c = ∠TQR = 35°

Since SR = ST, ΔRST is isosceles.

∴ ∠b = 180 - 35 - 35 = 180 - 70 = 110°

Hence, ∠a = 70°, ∠b = 110° and ∠c = 35°.