Question

15. In the given figure, PQ and PR are tangents of the circle. What is the measure of angle QPR?​

Answer 1

The measure of angle QPR is 96°.

Given:

Angle PQR=42°

To find:

Angle QPR

Solution:

The given tangents, PQ and PR, are of equal length.

SO, PQ=PR.

This implies that the measure of angles PQR and PRQ are equal. (angles corresponding to equal sides)

Angle PQR=Angle PRQ=42°

Now, in ΔPQR,

Angle PQR+angle PRQ+angle QPR=180°

Using the values,

42°+42°+angle QPR=180°

84°+angle QPR=180°

Angle QPR=180°-84°

Angle QPR=96°

Therefore, the measure of angle QPR is 96°.