Question

in the adjoining figure AB and CD are two equal chords of a circle with Centre O.OP and Q are perpendiculars on chords A B and C D respectively if angle POQ equals to 150 degree then find angle in APQ

Answer 1

this answer can help you

Answer 2

Given:

Angle POQ=150°

To find:

The measure of angle APQ

Solution:

The measure of angle APQ is 75°.

We can find the angle by following the given steps-

We know that the sum of all the angles of a triangle is 180°.

Since OP and OQ are perpendiculars, the angles OPA and OQC are equal to 90°.

Angle OPA=angle OQC=90°

Now, in ΔPOQ,

angle OPQ+angle OQP+angle POQ=180°

The chords AB and CD are at equal distance from the centre of the circle.

So, the perpendicular distance from the centre to the chord is also equal.

OP=OQ and angle OPQ=angle OQP (Angles corresponding to equal sides are also equal)

So, 2×angle OPQ+angle POQ=180°

2(angle OPQ)+150°=180°

2(angle OPQ)=180°-150°

2(angle OPQ)=30°

Angle OPQ=30/2

Angle OPQ=Angle OQP=15°

We know that the angle OPA=90°

Angle OPA=Angle OPQ+Angle APQ

90°=15°+Angle APQ

Angle APQ=90°-15°

Angle APQ=75°

Therefore, the measure of angle APQ is 75°.