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

Question

asked Dec 3, 2023 153k views

1 Answer

Limekin · Answer 1 · 2023-12-08T16:32:55+0000

Answer:

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
from both sides to isolate the variable gives us

10x-28=52 .

Then, adding
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
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

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