Question

What is the measure of angle R?

Answer 1

`m\angle R=37^(\circ)`

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.