Vertical/Complementary/Supplementary Angles

Name:______Date:______Period:_____

Vertical/Complementary/Supplementary AnglesMs. 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?