Question

If P is the incenter of triangle JKL, find the measure of JKP.

Answer 1

Answer:

m∠JKP = 31.5°

Step-by-step explanation:

Incenter of a triangle is the point where all the bisectors of interior angles intersect each other.

JN is the angle bisector of ∠KJL.

Therefore, m∠KJN = m∠LJN

(7x - 6) = (5x + 4)

7x - 5x = 6 + 4

2x = 10

x = 5

m∠KJN = (7x - 6)

            = 7(5) - 6

            = 35 - 6

            = 29°

In ΔKJN,

m∠JKN + m∠KNJ + m∠NJK = 180°

m∠JKN + 90° + 29° = 180°

m∠JKN = 180°- 119° = 61°

Since KO is the angle bisector of ∠JKN,

m∠JKP = $\frac{1}{2}(\angle JKN)$

            = $\frac{1}{2}(61)$

            = 30.5°