SOLUTION: two vertical angles are supplementary. find the measure of each angle.

Question 117475: two vertical angles are supplementary. find the measure of each angle.
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
There are two things you know about the vertical angles. The first thing is that this problem
tells you they are supplementary. That means that the measures of the two angles add up to be
180 degrees. Let mA represent the measure of vertical angle A and let mB represent the measure
of vertical angle B. Since, according to the problem, the two angles are supplementary,
you can write the supplementary angle equation:
.
mA + mB = 180
.
The other thing you can tell from geometry is that a pair of vertical angles will have equal
measures. For this case, since A and B are vertical angles we can say that mA = mB.
.
You can return to the supplementary angle equation:
.
mA + mB = 180
.
and substitute mA for mB since the two are equal. After this substitution the supplementary
angle equation becomes:
.
mA + mA = 180
.
The two terms on the left side add together to give:
.
2*mA = 180
.
To solve for mA, divide both sides by 2 to give:
.
mA = 180/2 = 90 degrees
.
and since mA = mB you know that the two vertical angles in this problem both have measures
of 90 degrees.
.
Hope this helps you to understand the problem and how it can be solved. If you need assistance
with understanding vertical angles and what they are, you can go to Wikipedia (the online
encyclopedia) and look up "vertical angles." That source has a description and drawing that
shows vertical angles.
.
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