Question

QR is tangent to circle P at point Q.

Circle P is shown. Line segment P Q is a radius. Line segment Q R is a tangent that intersects the circle at point Q. A line is drawn from point R to point P and goes through a point on the circle. Angle Q P R is 53 degrees.

What is the measure of angle R?

Answer 1

fig. 1.1 & 1.2 Calculation of the question. & fig of question.

Answer :-

The measure of angle R is 90°.

Calculation :-

Ref. to the figure 1.1 in attachment.

Answer 2

Given:

QR is a tangent to a circle with centre P at point Q.

PQ is the radius.

A line is drawn from point R to point P and goes through a point on the circle.

∠QPR=53°

To Find:

∠R.

Solution:

PQ is perpendicular to QR.

As, radius of a circle is always perpendicular to its tangent.

∠PQR=90°.

Now, in ΔPQR,

∠RQP+∠RPQ+∠PRQ=180°(Angle sum property)

⇒90°+53°+∠PRQ=180°

⇒∠PRQ=180°-(90+53)°

⇒∠PQR=37°

Therefore, the measure of angle R=37°.