Question

in the figure find <PQB, if O is the centre of circle.

Answer 1

as the angle at o is 90 degree this is a square and angle qpb = 180 - 42 - 90 = 48
therefore angle PBQ = 48
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Answer 2

Given:

Angle PBA=42°

To find:

The measure of angle PQB

Solution:

The angle PQB is equal to 48°.

O is the circle's centre with AB as the diameter and angle PBA=42 degrees.

The angle APB in the semi-circle is a right angle.

So, angle APB=90°

Now in ΔAPB, angle APB+angle PBA+angle PAB=180° (Sum of angles)

Using the values, we get

90°+42°+angle PAB=180°

132°+angle PAB=180°

Angle PAB=180°-132°

Angle PAB=48°

Now, the chord PB is making two angles, angle PAB and angle PQB.

Angle PAB=Angle PQB (Angles from the same chord)

So, angle PQB=48°

Therefore, the angle PQB is equal to 48°.