Answer Key — Unit 3
1.
They are complementary and add up to 90
◦
.
2.
3.
∠
a
= 59
◦
,
∠
b
= 82
◦
4.
x
= 64
◦
5.
x
= 56
◦
6.
x
= 48
◦
7.
x
= 55
◦
8.
No, this would only work if the angle is equal to 0. If
x
= 1, then the complement
is 89
◦
and the supplement would be 179
◦
.
Half the measure of the supplement
would be=
1
2
(179) = 89
.
5, which is greater than the complement.
9.
In the following picture, the consecutive angles formed by two straight lines are all
supplementary. This means that
m
∠
A
+
m
∠
B
= 180, and
m
∠
B
+
m
∠
C
= 180.
Since A and C share angle B,
m
∠
A
should equal
m
∠
B
. The same would be the
case with angles A, D, and C, or any other combination of 3 consecutive angles.
10.
m
∠
AOC
= 70
◦
11.
a)
m
∠
1 = 33
◦
b)
m
∠
1 = 70
◦
c)
x
= 22
, y
=
72
5
12.
a)
x
= 50
, y
= 20
b)
x
= 30
, y
= 70
13.
m
∠
TAC
=
m
∠
ACB
+
m
∠
ABC
; pictures will vary.
14.
a)
70
◦
,
49
◦
,
61
◦
b)
80
◦
,
70
◦
,
150
◦
15.
a)
56
◦
,
68
◦
b)
62
◦
,
62
◦
16.
a)
m
∠
CBD
= 36
◦
, m
∠
DBA
= 36
◦
, m
∠
BCD
= 72
◦
, m
∠
BDC
= 72
◦
, m
∠
BDA
=
108
◦
, m
∠
BAC
= 36
◦
b)
CD
= 1

x
17.
m
∠
C
= 36
◦
18.
x
=
180
7
19.
m
∠
Q
= 54
◦
, m
∠
R
= 36
◦
20.
AB
is the largest side since
∠
C
is the largest angle.
The longest side is always
opposite the largest angle.
21.
m
∠
CFD
= 63
◦
22.
Triangle BDE is isosceles because the two base angles (