Answers:
x = 6
Each angle is 45 degrees
The diagram is shown below
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Step-by-step explanation:
Vertical angles are always congruent
Set the two expressions equal to each other and solve for x.
5x+15 = 3x+27
5x-3x = 27-15
2x = 12
x = 12/2
x = 6
As a way to check the answer, replace x with 6 in each expression. We should get the same thing on both sides
5x+15 = 3x+27
5*6+15 = 3*6+27
30+15 = 18+27
45 = 45
Each angle is 45 degrees, so the answer is confirmed.
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The diagram is shown below. There are infinitely many ways to draw out the diagram. In the version I drew, the angles aren't vertically aligned but instead they are opposite one another in this X configuration. So the vertical angles could be vertically aligned, but they don't have to be.
In short: draw an X shape and mark any two opposite angles to form the vertical angles.