Question

Hlo guys I need step by step solution please it's a 10 class question please help me

Answer 1

Answer:

angle PRQ = 120 degrees

Explanation:

Looking at the figure I can make out a few things

angle OPT = 90 degrees    (OP is a radius to the tangent T)

angle QPT = 60 degrees   (given)

angle OPQ = 90 - 60 = 30 degrees

angle OQP = OPQ = 30 degrees  (OP = OQ, both are radii)

Now in triangle OPQ,

angle POQ = 180 - 30 - 30  = 120 degrees   (angle POQ = 180 - OQP - OPQ

Now ext. angle POQ = 360 - 120 = 240 degrees

And now from Circle Theorem no. 5,

ext angle POQ = 2 x angle PRQ

240 = 2 x PRQ

thus angle PRQ = 120 degrees

good day

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Answer 2

Explanation:

given:- PT is a tangent to circle with centre O,also angle QPT =60°

Since we know tangent is perpendicular to radius,

THEREFORE,. ANGLE OPT =90°

SO, ANGLE QPO=30°

since OP=OQ

So,. angle OPQ = angle OQP = 30°

Therefore by angle sum property in ∆OPQ

angle POQ will be 120°

so,

reflex angle POQ = 240°

Now, we know angle subtended by major arc at centre is twice the angle subtended by end point of arc on remaining circle

so,. angle POQ = 2 × angle PRQ

i.e.

240° =2 × angle PRQ

i.e.

【angle PRQ = 120°】

HOPE IT HELPS