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Geometry 1A
Name ________________________
Homework
5.1
1. Find the m∠1 .
o
117
o
33
1
Find the value of each variable.
2.
3.
w
o
40
o
t
o
30
o
o
80
4.
x
o
o
z
o
30
o
70
o
30
o
y
5.
o
40
x
o
y
o
o
a
o
6.
7.
x
o
o
30
2x
o
c
o
If possible, draw a triangle to fit each description. Mark the triangles to show known information. If
no triangle can be drawn, write not possible and explain why.
8. equilateral right
9. obtuse isosceles
10. acute isosceles
11. scalene acute
12. Reason Abstractly: Two remote interior angles of a triangle measure 37o and 62o. What is
the measure of the exterior angle associated with the remote interior angles? What is the
measure of the third angle of the triangle? Show all necessary work.
13. Find m∠2 .
o
13
o
128
2
Find the values of the variables and then the measures of the angles. Classify each triangle by its
angles.
U
14.
15.
C
o
75
(2x + 4)
x
o
o
B
(2x – 9)
o
x
o
T
V
A
x = ______ m∠A =_____, m∠B =_____
m∠T =_____, m∠U =_____, m∠V =______
Classify: _______________
Classify: _______________
16. Find the values of the variables.
E
eo
o
do
F
32
bo
co
o
55
H
ao
G
17. What is the measure of each angle of an equilateral triangle? Explain.
18. Is every equilateral triangle isosceles? Is every isosceles triangle equilateral? Explain.
19a. The ratio of the angle measures in ∆BCR is 2: 3: 4. Find the angle measures.
b. What type of triangle is ∆BCR ?
20. Find m∠3 if m∠5 =
130 and m∠4 =
30 .
5
2
4
3
Use for #20-21
1
21. Find m∠2 if m∠3 =
125 and m∠4 =
23 .
Answer Key
1.
2.
3.
4.
5.
6.
7.
8.
9.
30
x = 70; y = 110; z = 30
t = 60; w = 60
x = 80; y = 80
70
30
60
Not possible; a right triangle will always
have one longest side opposite the
right angle.
10.
11. o
12. 99 , 81o
13. 115
14. x = 52.5; m∠A =
52.5o, m∠B = 52.5o;
acute
15. x = 37; m∠T = 65o, m∠U = 78o,
m∠V = 37o; acute
16. a = 67, b = 58, c = 125, d = 23, e = 90
17. Answers will vary.
18. Answers will vary.
19. a. 40o, 60o, 80o; b. acute
20. 100o
21. 32o