Question

What is m∠JNM?



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°

Answer 1

Since they are vertical angles, they are congruent to each other.
Thus, 4x+6=7x-21
Solve for x and get:
x=9
Plug that into the equation that matches the angle and get: 42

Answer 2

we know that

Vertical angles are a pair of opposite and congruent angles formed by intersecting lines

In this problem

m∠JNM=m∠KNL -------> by vertical angles

so

`(4x+6)\°=(7x-21)\°`

Solve for x

`7x-4x=6+21\\3x=27\\x=9\°`

Find the value of m∠JNM

m∠JNM=
`(4x+6)\°`

substitute the value of x

m∠JNM=
`(4*9+6)\°`

m∠JNM=
`42\°`

therefore

the answer is

m∠JNM=
`42\°`