Question

What is the measure of angle R?

Answer 1

Answer:

$m\angle R=37^{\circ}$

Step-by-step explanation:

We have been given a diagram of a circle. We are asked to find the measure of angle R.

Since QR is the tangent of our given circle, so measure of angle Q will be 90 degrees as radius is perpendicular to tangent at point of tangency.

Now, we will use angle sum property to solve for angle R as:

$m\angle P+m\angle Q+m\angle R=180^{\circ}$

$53^{\circ}+90^{\circ}+m\angle R=180^{\circ}$

$143^{\circ}+m\angle R=180^{\circ}$

$143^{\circ}-143^{\circ}+m\angle R=180^{\circ}-143^{\circ}$

$m\angle R=37^{\circ}$

Therefore, the measure of angle R is 37 degrees.