Question

If line segment jm bisects angle hjk, m angle hjm=8x+14, and m angle mjk = 11x-10, what is the measure of angle hjk?

Answer 1

Answer: $\angle HJK=156\textdegree$

Step-by-step explanation:

Since we have given that

JM bisects ∠HJK

As , we know that

if any ray bisects the angle it make it into two equal angles so, their measures will be equal ,

so,

$\angle HJM=\angle MJK\\\\8x+14=11x-10\\\\41+10=11x-8x\\\\24=3x\\\\\frac{24}{3}=x\\\\8\textdegree=x$

So, our required answer will given by

$\angle HJK=\angle HJM +\angle MJK\\\\\angle HJK=8x+14+11x-10\\\\\angle HJK=19x+4\\\\\angle HJK=19\times 8+4\\\\\angle HJK=156\textdegree$

So,

$\angle HJK=156\textdegree$