Download Scholarship Geometry Name: Worksheet section 1

Scholarship Geometry
Worksheet section 1-4
Name:
1. An angle measures xº. What is the measure of its complement? What is the measure of its
supplement?
2. <ABC and <CBD are adjacent angles. Which side do the angles have in common?
3. Write two pairs of vertical angles.
Tell whether the angles are only adjacent, adjacent
and form a linear pair, or not adjacent.
4. <1 and <4
5. <2 and <3
use for #4-7
6. <3 and <4
7. <3 and <1
Given m<A = 56.4º and m<B = (2x – 4)º, find the measure of each of the following.
8. the supplement of <A
9. the complement of <A
10. the supplement of <B
11. the complement of <B
12. 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.
13. In the tile pattern, <1  <2.
<1 and <3 are complementary and
<2 and <4 are complementary.
If m<1 = 22.3º, find m<2, m<3 and m<4.
(over)
14. Write at least four pairs (there are six in all)
of vertical angles.
15. 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?
In #16-18, <ABD and <BDE are supplementary. Find the measures of both angles. Show
all work for each.
16. m<ABD = 5x
m<BDE = 17x – 18
17. m<ABD = 3x + 12
m<BDE = 7x – 32
18. m<ABD = 12x – 12
m<BDE = 3x + 48
In #19-21, <ABD and <BDC are complementary. Find the measures of both angles. Show
all work for each.
19. m<ABD = 5y + 1
m<BDC = 3y – 7
20. m<ABD = 4y + 5
m<BDC = 4y + 8
21. m<ABD = y – 30
m<BDC = 2y
22. Explain in writing why an angle that is supplementary to an acute angle must be an obtuse
angle.
In #23-26, determine whether each statement is true or false. If false, explain why?
23. If an angle is acute, then its complement must be greater than its supplement.
24. A pair of vertical angles may also form a linear pair.
25. If two angles are supplementary and congruent, the measure of each angle is 90º.
26. If a ray divides an angle into two complementary angles, then the original angle is a right
angle.
(over)
CHALLENGE…
27. The supplement of an angle is 4 more than twice its complement. Find the measure of the
angle.
28. An angle’s measure is twice the measure of its complement. The larger angle is how many
degrees greater than the smaller angle?
29. The supplement of an angle is 36º less than twice the supplement of the complement of the
angle. Find the measure of the supplement.