Question

APB is a tangent to the circle with Centre O at the point P if angle QPB =50 degrees then measure of angle POQ

Answer 1

Refer to the attached image.

Given: APB is a tangent to the circle with Center O at the point P if angle QPB = 50 degrees

We have to find the measure of angle POQ.

Solution:

Since APB is a tangent to the circle O at point P.

By using the property of tangent which states that

"A tangent and radius make a 90 degree angle at the point of contact."

Hence, tangent PB forms right angle with radius OP.

Therefore, $\angle OPB = 90^\circ$

$\angle OPQ = \angle OPB - \angle QPB$

$\angle OPQ = 90^\circ - 50^\circ$

= $40^\circ$

Consider the triangle OPQ.

OP = OQ

(As Both are radius of the given circle, hence they are equal)

Therefore, $\angle OPQ = \angle OQP$

Opposite angles opposite to the equal opposite sides are always equal.

Now, by angle sum property which states

"The sum of all the angles of a triangle is 180 degrees".

$\angle OPQ+ \angle OQP + \angle QOP = 180^\circ$

$40^\circ+ 40^\circ + \angle QOP = 180^\circ$

$80^\circ + \angle QOP = 180^\circ$

$\angle QOP = 180^\circ - 80^\circ = 100^\circ$

Therefore, the measure of angle POQ is 100 degrees.

Answer 2

Step-by-step explanation:

see the attachment

Thank you