Question

What is the missing angle? (Please use image attached)

Answer 1

56

Explanation:

Since vertical angles are equal, we know the two angles labeled are equal.

We can then set up an equation to get

`19x-28=9x+52.`

Subtracting
`9x` from both sides to isolate the variable gives us

`10x-28=52`.

Then, adding
`28` to both sides gives

`10x=80,`

and dividing both sides by 10 gives

`x=8.`

Now, we can find the measure of
`9x+52` by plugging what we found for
`x` in:

`9(x)+52=9(8)+52=72+52=124.`

Since the angles ? and 9x+52 make up a line, they are supplementary. Therefore, we have

`?=180-(9x+52)=180-124=\boxed{56}.`