Question

please do this question​

Answer 1

We know that the radius and tangent are perpendicular at their point of contact :-

.°. Angle OPT = 90°

Now, Angle OPQ=Angle OPT=Angle QPT =90° - 60° = 30°

Since, OP = OQ as born in radius

.°.Angle OPQ = Angle OPQ = 30°

( Angles opposite to equal sides equal )

Now, In isosceles, POQ

Angle POQ + Angle OPQ + Angle OQP = 180°

( Angle sum property of a triangle )

=> Angles POQ = 180° - 30° - 30° = 120°

Now,

Angle POQ + reflex Angle POQ = 360°

(Complete Angle)

reflex Angle POQ = 360° - 120° = 240°

We know that the angle subtended by an arc at the centre bouble the angle subtended by the arc at any point on the remaining part of the circle

.°. Angle PRQ = 1/2( reflex Angle POQ) = 120°.

_Answer Completed _

Answer 2

Answer:

50

Step-by-step explanation:

140 = qrp + rpq

External angle = sum of internal angles

140 = prq +90

Prq = 140-90=50