Question

Use the properties of vertical angles to find the value of x.
Responses
A 33
B 55
C 77
D 99
Question 2
What is the measure of ∠A?
Responses
A 157°157°
B 159°159°
C 161°161°
D 163°

Answer 1

I don’t have the diagram or the angle expressions, so I can’t pick a choice yet. Please either upload the figure or type the angle expressions (for example “one angle is 2x+5 and the vertical angle is 3x−12”) and I’ll solve it.

Meanwhile, here’s the method so you can check quickly:

1. Property: vertical (opposite) angles are equal. If two vertical angles are given by expressions in x, set them equal.
Example: if angles are 2x + 5 and 3x − 12, solve 2x + 5 = 3x − 12 → x = 17.
2. If the question asks for the angle measure after finding x, substitute x back into one of the expressions: 2(17)+5 = 39°.
3. If the diagram involves a linear pair (adjacent angles on a straight line), those two are supplementary: set their sum = 180°.

Send the diagram or the expressions and I’ll pick the correct choice(s) and show the work.