Download Worksheet 1-5 For #1-4, use the diagram to determine if each

Scholarship Geometry
Worksheet 1-5
Name:
For #1-4, use the diagram to determine if each statement is true or false. Briefly explain.
1. <1 and <5 are adjacent angles.
2. <3 and <5 are vertical angles.
3. <3 and <4 are complementary.
use for #1-4
4. <1 and <2 are supplementary.
Write an angle or angles in the diagram described by each of #4-9.
5. supplementary to <AOD
6. adjacent and congruent to <AOE
7. supplementary to <EOA
8. complementary to <EOD
9. a pair of vertical angles
use for #5-9
For #10-17, can you make each conclusion from the information in the diagram? Answer
yes or no and be prepared to explain your answer.
10. <J  <D
11. <JAC  <DAC
12. m<JCA = m<DCA
13. m<JCA + m<ACD = 180
14. AJ  AD
15. C is the midpoint of JD
use for #10-17
16. <JAE and <EAF are a linear pair.
17. <EAF and <JAD are vertical angles.
18. Write two pairs of angles that from a linear pair in the diagram.
(over)
In #19-20, <ABD and <DBE are form a linear pair. Find the measures of both angles.
Show all work for each.
19. m<ABD = 5x
m<DBE = 17x – 18
20. m<ABD = 3x + 12
m<DBE = 7x – 32
In #21-22, <ABD and <DBC are complementary. Find the measures of both angles. Show
all work for each.
21. m<ABD = 5y + 1
m<DBC = 3y – 7
22. m<ABD = y – 30
m<DBC = 2y
For #23-26, BD bisects <ABC. Find the value of x and m<ABC. Show all work. A sketch
may help.
23. m<ABD = 5x, m<DBC = 3x + 10
24. m<ABC =
5
x , m<ABD = x + 5
2
25. m<ABD = 4x – 16, m<CBD = 2x + 6
26. m<ABD = 3x + 20, m<CBD = 6x – 16
27. An angle’s measure is 3 times the measure of its complement. Find the measure of the angle
and the measure of its complement. Show all work.
28. The angle measures 30º, 60º, 120º and 150º are written on slips of paper. You choose two
slips of paper at random. What is the probability that the angle measures are
supplementary?
29. Explain in writing why an angle that is supplementary to an acute angle must be an obtuse
angle.
30. If an angle is acute, then its complement must be greater than its supplement. Show a
specific example of why this statement is false.
(over)
CHALLENGES…
31. The supplement of an angle is 4 more than twice its complement. Find the measure of the
angle.
32. An angle’s measure is twice the measure of its complement. The larger angle is how many
degrees greater than the smaller angle?
33. The supplement of an angle is 36º less than twice the supplement of the complement of the
angle. Find the measure of the supplement.