What is the measure of angle R?

Question

asked Oct 28, 2019 204k views

1 Answer

Mcrute · Answer 1 · 2019-11-02T21:35:54+0000

Answer:

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

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.