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Vertical Angles - Problem 1
Vertical angles are angles that are congruent and share a common vertex. Since they are congruent, the measure of their angles is the same. So, when finding the measure of an angle, you have also found the measure of an angle vertical to it.
Recall that the sum of the three angles in a triangle is 180°. So, if given two angles that are 30° and 45°, then 180° - 30° - 45° = 105°. So, the sum of the third angle is 105°. Since this angle is vertical to another, the measure of the other angle is also 105°.
The reason why you learned about vertical angles is so you can find missing angles. In a problem like this you’re going to find x by finding this angle right here. You know that vertical angles share a common vertex and they must be congruent.
So the key thing here is remembering that the three angles of a triangle must sum to 180 degrees. If I look at these two angles 30 and 45, well that’s 75 and if I take 75 away from 180, I get 105. So I know that this angle right here must be 105 degrees, since x is a vertical angle with 105 degrees, x must equal 105 degrees.
The key thing here is to remember that vertical angles are congruent and we found this angle by remembering the three angels in a triangle must sum to 180 degrees.