Question

Plz solve it
Plz
PQ is a tangent from an external point P to a circle with Centre O and OP cuts the circle at T and QOR is a diameter if angle POR is equal to 130 degree and S is a point on circle find angle1 +2

Answer 1

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SOLUTION _____________

Given — PQ is a Tangent..... QOR is the diameter..... Angle POR = 130°

To Find — Angle 1 & 2

SOLVING FOR ANGLE 1

We know that radius is perpendicular to tangent

So, Angle PQO = 90°

Now,

Angle POR + Angle POQ = 180° ( Linear pair angle)

130° + Angle POQ = 180°

Angle POQ = 180° – 130°

Angle POQ = 50°

Now, In ∆ POQ

Angle 1 + Angle PQO + Angle POQ = 180°

Angle 1 = 180° – (90° + 50°)

Angle 1 = 180° – 140°

Angle 1 = 40°

Now, SOLVING FOR ANGLE 2

Look at SRT

We have, The angle subtended by an arc at the centre is double the angle subtended by it any point on the remaining part of the circle

By this Property

Angle subtended at centre = 130°

Angle subtended at Circumference = Angle 2

We know,

2(Angle 2) = 130°

Angle 2 = 130°/2

Angle 2 = 65°

1 = 40° & 2 = 65°

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