Question

In the given figure, find angle QSR.
please help answer with explanation required!!!​

Answer 1

Answer:

50° is the answer.

angle QOR=100°

angle QSR=1/2 angle QOR

THUS , QSR=50°

Answer 2

The measure of angle QSR is 65°.

Given:

Angle QPR=50°

To find:

Angle QSR

Solution:

The lines PQ and PR are the circle's tangents and thus, perpendicular to the radius.

So, angle OQP=angle ORP=90°

Now, in quadrilateral OQPR,

angle OQP+angle ORP+angle QPR+angle QOR=360°

Using values,

90°+90°+50°+angle QOR=360°

230°+angle QOR=360°

angle QOR=360°-230°

angle QOR=130°

Now, the angles minor QOR and major QOR=360°.

So, the major angle QOR=360°-130°=230°.

We know that the angle QTR is at the circumference and thus, its measure is half of the major angle QOR.

Angle QTR=Major angle QOR/2=230°/2=115°

In the cyclic quadrilateral QTRS, angle QTR+ angle QSR=180°.

Using values,

115°+angle QSR=180°

Angle QSR=180°-115°

Angle QSR=65°

Therefore, the measure of angle QSR is 65°.