Remember that if two angles are vertical, they are congruent and share a common vertex. If they are congruent, then they have the same measure, so they can both be labeled with the same variable x. Also remember that if angles are supplementary, their measures add up to 180°. This means that x + x = 180°, or, 2x = 180°. By solving for x, you see that x = 90°, so both of these angles are right angles.
A lot of times in geometry you’ll be asked to put together two different vocabulary words. Here it says if two angles are vertical, which we know means that they share a common vertex and congruent, and supplementary which is commonly confused with complementary, supplementary means they sum to 180 degrees, what must be their measurement?
Well like a good geometry student I’m going to draw a picture. So I’m going to draw two intersecting lines forming two pairs of vertical angles. I’m going to label both of these x, why did I do that? Because I know they have to be the same number. Since they’re vertical they have to be congruent, since they’re supplementary x plus x must equal 180 degrees, again that’s the definition of supplementary.
Well x and x if I combine those is not x², it’s 2x and I get 180 degrees. So I’m going to divide by 2 and I see that x must be 90 degrees. Which means what must be the measurement, they must both be right angles since they’re congruent and they sum to 180 degrees.