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`

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\\\\(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* 8+4\\\\\angle HJK=156\textdegree`

So,

`\angle HJK=156\textdegree`