The measure of angle PJM, which is equivalent to NQ, is 136° and the measure of angle PLQ is 22°, as Q is the incenter of Triangle JKL.
We are given that Q is the incenter of Triangle JKL.
This means that the angle bisectors of the triangle's angles meet at point Q, forming three smaller interior angles at this point.
We are also given that angle MKN equals 94° and angle PJQ equals 22°.
Now, the incenter of a triangle divides the opposite angle into two angles that are equal.
Since point Q is the incenter, angle PJQ will be equal to angle PLQ, which means angle PLQ also measures 22°.
By knowing that the sum of the internal angles of a triangle equals 180°, we can calculate the measure of angle PJM by subtracting the sum of angles PJQ and PLQ from 180°:
Measure of angle PJM = 180° - (angle PJQ + angle PLQ) = 180° - (22° + 22°) = 180° - 44° = 136°.
Therefore, measure of angle PJM, which is equivalent to NQ, and measure of angle PLQ are 136° and 22°, respectively.
The probable question may be:
The angle bisectors of Triangle JKL are JQ, KQ, and LQ. They meet at a single point Q.
(In other words, Q is the incenter of Triangle JKL.)
Suppose MQ = 14, LQ = 17, measure of angle MKN = 94°, and measure of angle PJQ=22°.
Find the following measures.
Note that the figure is not drawn to scale.
measure of angle PJM=
NQ=
measure of angle PLQ=