Question

Point K is the incenter of triangle PQR. what is m

Answer 1

115 degrees

Explanation:

The incenter is where the angle bisectors of a triangle meet. So
`m\angle{PQK}=15^\circ \text{ and } m\angle{PQR}=30^\circ`.

To find the measure of angle RKQ, we need to find the measure of angle PRQ. In the big triangle, the sum of angle measures is 180 degrees, and we know two of the angles, 50 deg and 30 deg (for a total of 80 deg). That leave 100 degrees for the measure of angle PRQ.

But RK is an angle bisector, so
`m\angle{KRQ}=50^\circ`.

We now know two of the angles in
`\triangle{KRQ}`, 50 deg and 15 deg. Those total 65 degrees, so
`m\angle{RKQ}=180^\circ - 65^\circ=115^\circ`