Name:__________________________
Date:______ Period:_____
Vertical/Complementary/Supplementary Angles
Ms. Anderle
Vertical/Complementary/Supplementary Angles
In Geometry, there are many types of relationships that involve angles. Most of these
relationships involve pairs of angles.
Special Angle Pairs:
1. Adjacent Angles: these are two angles that lie in the same plane and share a common
vertex and a common side. They do not share any common interior points. We can describe
these two angles are being "next to" each other. The sum of two adjacent angles is equal
to the whole angle.
Example:
2. Linear Pair: a specific type of adjacent angle with noncommon sides as opposite rays.
Opposite rays make up a line. Therefore, these angles are supplementary and add up to
180˚.
Example:
3. Vertical Angles: two nonadjacent angles formed by intersecting lines. These angles
"look at" each other. Vertical angles are congruent.
Example:
4. Complementary Angles: two angles that add up to 90˚.
Examples:
5. Supplementary Angles: two angles that add up to 180˚.
Examples:
Problems:
1. <ABC and <XYZ are complementary. If m<ABC = 70˚, then what is the m<XYZ?
2. If the m<ABC = 85˚, use the diagram below to find the value of x.
3. Two complementary angles measure 2x+10 and x+10 degrees. What is the value of x?
4. Two supplementary angles measure 5x-30 and x+90 degrees. What is the value of x?
5. <1 and <2 are vertical angles. If m<1 = 120˚ and m<2 = 2x-10, what is the value of x?
6. Angles <A and <B form a linear pair. If m<A = 2x and m<b = 4x+108, find the value of x.
Find the measure of each angle.
7. Use the diagram below to find the values of x and y.
8. Use the diagram below to find the values of x and y.
9. <ABC and <CBD form a linear pair. If m<ABC = 2y+50 and m<CBD = 5y-17, then what is
the value of y?
10. Find the measures of two supplementary angles if the difference in the measures of
the two angles is 18.
11. A pair of supplementary angles are in the ratio 1:2. How many degrees are in the larger
angle?
12. If the measure of a pair of complementary angles are in the ratio of 4:11, what is the
measure of larger angle?
13. <3 and <4 form a linear pair. The measure of <3 is four more than three times the
measure of <4. Find the measure of each angle.
14. The measure of an angle's supplement is 76 less than the measure of the angle. Find
the measure of the angle and its supplement.
15. <E and <F are supplementary. The measure of <E is 54 more than the measure of <F.
Find the measures of each angle.
16. <J and <A are vertical angles. If the m<J = 3x+20 and the m<A = 5x-50, then what is
the value of <J?
17. Two angles are supplementary. If one angle is six more than three times the other,
what is the measure of each angle?
18. Angles RPL and LPH are adjacent angles. If m<RPL = x – 5, m<LPH = 2x + 18, and the
m<RPH = 58, what is the measure of <LPH?
19. Angles RPL and LPH are adjacent angles. If m<RPL = x + 2, m<LPH = 5x – 6, and the
m<RPH = 86, what are the measures of <RPL and <LPH?
20. Angles RPL and LPH are adjacent angles. If m<RPL = 6z – 4, m<LPH = 2z + 20, and the
m<RPH = 112, what are the measures of <RPL and <LPH?