1
,CHAPTER 1 cn
Section 1.1 Solutions --------------------------------------------------------------------------------
cn cn cn
1
x 1 x
c n c n c n cn c n c n c n
1. Solve for x:
c n cn cn c n cn 2. Solve for x:
c n cn cn c n cn
2 360∘ 4 360∘
360∘ 2x, so that x 180∘ .
cn cn c n cn c n cn cn cn 360∘ 4x, so that x 90∘ .
c n cn c n cn c n cn cn cn
1 x 2
x
3. Solve for x: 4. Solve for x:
cn c n c n c n c n c n
c n cn cn c n cn cn c n cn cn c n c n cn
3 360∘ 3 360∘
360∘ 3x, so that x 120∘ . (Note
cn cn cn cn c n cn cn cn cn 720∘ 2(360∘ ) 3x, so that x 240∘ .
cn cn cn cn cn cn cn c n cn cn cn cn
: The angle has a negative measure si
cn cn cn cn cn cn cn (Note: The angle has a negative measu
c n cn cn cn cn c n
nce it is a clockwise rotation.)
cn cn cn cn cn re since it is a clockwise rotation.)
cn cn cn cn cn cn
x 5 7 x
c n c n c n cn cnc n c n c n
5. Solve for x:
c n cn cn c n cn 6. Solve for x:
c n cn cn c n cn
6 360∘ 12 360∘
1800∘ 5(360∘ ) 6x, so that x 300∘ .
cn cn cn cn cn cn cn c n cn cn cn 2520∘ 7(360∘ ) 12x, so that x 210∘ .
cn cn cn cn cn cn cn c n cn cn cn
4 x x 5
7. Solve for x: 8. Solve for x:
cn c n c n c n c n c n c n
c n cn cn c n cn cn c n cn cn c n cn cn
5 360∘ 9 360∘
1440∘ 4(360∘ ) 5x, so that
cn cn cn cn cn cn cn 1800∘ 5(360∘ ) 9x, so that
cn cn cn cn cn cn cn
x 288∘ .
cn cn cn x 200∘ .
cn cn cn
(Note: The angle has a negative meas
c n cn cn cn cn cn (Note: The angle has a negative measur
c n cn cn cn cn cn
ure since it is a clockwise rotation.)
cn cn cn cn cn cn e since it is a clockwise rotation.)
cn cn cn cn cn cn
9. 10.
a) complement: 90∘ 18∘ 72∘ c n cn c n c n a) complement: 90∘ 39∘ 51∘ c n cn cn c n c n
b) supplement: 180∘ 18∘ 162∘ c n cn c n c n b) supplement: 180∘ 39∘ 141∘ c n cn cn c n c n
11. 12.
a) complement: 90∘ 42∘ 48∘ c n cn cn c n c n a) complement: 90∘ 57∘ 33∘ c n cn cn c n c n
b) supplement: 180∘ 42∘ 138∘ c n cn cn c n c n b) supplement: 180∘ 57∘ 123∘ c n cn cn c n c n
2
, Section 1.1 cn
13. 14.
a) complement: 90∘ 89∘ 1∘ c n cn cn c n c n a) complement: 90∘ 75∘ 15∘ c n cn cn c n c n
b) supplement: 180∘ 89∘ 91∘ c n cn cn c n c n b) supplement: 180∘ 75∘ 105∘ c n cn cn c n c n
15. Since the angles with measures 4x∘ and 6x∘ are assumed to be complemen
c n cn cn cn cn cn c n c n cn cn cn cn cn
tary, we know that 4x∘ 6x∘ 90∘. Simplifying this yields
cn cn cn cn cn cn cn cn c n cn cn
10x∘ 90∘, cn cn cn c n so that x 9. So, the two angles have measures 36∘and 54∘ .
cn c n cn cn c n cn cn cn cn cn c n cn cn
16. Since the angles with measures 3x∘ and 15x∘ are assumed to be supplemen
c n cn cn cn cn cn c n c n cn cn cn cn cn
tary, we know that 3x∘ 15x∘ 180∘. Simplifying this yields
cn cn cn cn cn cn cn cn c n cn cn
18x∘ 180∘, so that cn cn cn cn cn x 10. So, the two angles have measures 30∘ and 150∘ .
cn cn c n cn cn cn cn cn c n cn cn cn
17. Since the angles with measures 8x∘ and
c n cn cn cn cn c n cn c n 4x∘ are assumed to be supplementa cn cn cn cn cn
ry, we know that 8x∘ 4x∘ 180∘. Simplifying this yields
cn cn cn cn cn cn cn cn c n cn cn
12x∘ 180∘, cn cn c n so that x 15. So, the two angles have measures 60∘ and 120∘ .
cn cn cn cn c n cn cn cn cn cn c n cn cn cn
18. Since the angles with measures 3x 15∘and 10x 10∘are assumed to be co
c n cn cn cn cn c n cn cn c n cn cn cn cn cn cn
mplementary, we know that 3x 15∘ 10x 10∘ 90∘. Simplifying this yields cn cn cn cn cn cn cn cn cn cn c n cn cn
13x 25∘ 90∘, cn cn cn cn cn so that 13x∘ 65∘ and thus, x 5. So, the two angles have meas
cn cn cn cn c n cn c n cn cn c n cn cn cn cn cn
ures 30∘and 60∘ .
c n cn cn
19. Since 180∘, we know th
c n cn cn cn cn cn c n cn c n cn cn 20. Since 180∘, we know th
c n cn cn cn cn cn c n cn c n cn cn
at at
1 17∘ –33∘ 180∘ and so, 30∘ . 1 10∘ –45∘ 180∘ and so, 25∘ .
– –
cn cn cn cn cn cn cn c n cn cn cn cn cn cn cn cn cn cn cn cn cn cn
cn cn
cn150∘ cn155∘
21. Since 180∘, we know th
c n cn cn cn cn cn c n cn c n cn cn 22. Since 180∘, we know th
c n cn cn cn cn cn c n cn c n cn cn
at at
4 180∘ and so, 30∘.
cn cn cn cn cn cn cn cn cn cn cn cn cn 3 180∘ and so, 36∘.
cn cn cn cn cn cn cn cn cn cn cn cn cn
–– –– –– ––
cn6cn cn5
Thus, 4 120∘ and 30∘ .
c n cn cn c n cn c n cn c n cn c n cn cn Thus, 3 108∘ and 36∘ .
c n cn cn c n cn c n cn c n cn c n cn cn
3
,
,CHAPTER 1 cn
Section 1.1 Solutions --------------------------------------------------------------------------------
cn cn cn
1
x 1 x
c n c n c n cn c n c n c n
1. Solve for x:
c n cn cn c n cn 2. Solve for x:
c n cn cn c n cn
2 360∘ 4 360∘
360∘ 2x, so that x 180∘ .
cn cn c n cn c n cn cn cn 360∘ 4x, so that x 90∘ .
c n cn c n cn c n cn cn cn
1 x 2
x
3. Solve for x: 4. Solve for x:
cn c n c n c n c n c n
c n cn cn c n cn cn c n cn cn c n c n cn
3 360∘ 3 360∘
360∘ 3x, so that x 120∘ . (Note
cn cn cn cn c n cn cn cn cn 720∘ 2(360∘ ) 3x, so that x 240∘ .
cn cn cn cn cn cn cn c n cn cn cn cn
: The angle has a negative measure si
cn cn cn cn cn cn cn (Note: The angle has a negative measu
c n cn cn cn cn c n
nce it is a clockwise rotation.)
cn cn cn cn cn re since it is a clockwise rotation.)
cn cn cn cn cn cn
x 5 7 x
c n c n c n cn cnc n c n c n
5. Solve for x:
c n cn cn c n cn 6. Solve for x:
c n cn cn c n cn
6 360∘ 12 360∘
1800∘ 5(360∘ ) 6x, so that x 300∘ .
cn cn cn cn cn cn cn c n cn cn cn 2520∘ 7(360∘ ) 12x, so that x 210∘ .
cn cn cn cn cn cn cn c n cn cn cn
4 x x 5
7. Solve for x: 8. Solve for x:
cn c n c n c n c n c n c n
c n cn cn c n cn cn c n cn cn c n cn cn
5 360∘ 9 360∘
1440∘ 4(360∘ ) 5x, so that
cn cn cn cn cn cn cn 1800∘ 5(360∘ ) 9x, so that
cn cn cn cn cn cn cn
x 288∘ .
cn cn cn x 200∘ .
cn cn cn
(Note: The angle has a negative meas
c n cn cn cn cn cn (Note: The angle has a negative measur
c n cn cn cn cn cn
ure since it is a clockwise rotation.)
cn cn cn cn cn cn e since it is a clockwise rotation.)
cn cn cn cn cn cn
9. 10.
a) complement: 90∘ 18∘ 72∘ c n cn c n c n a) complement: 90∘ 39∘ 51∘ c n cn cn c n c n
b) supplement: 180∘ 18∘ 162∘ c n cn c n c n b) supplement: 180∘ 39∘ 141∘ c n cn cn c n c n
11. 12.
a) complement: 90∘ 42∘ 48∘ c n cn cn c n c n a) complement: 90∘ 57∘ 33∘ c n cn cn c n c n
b) supplement: 180∘ 42∘ 138∘ c n cn cn c n c n b) supplement: 180∘ 57∘ 123∘ c n cn cn c n c n
2
, Section 1.1 cn
13. 14.
a) complement: 90∘ 89∘ 1∘ c n cn cn c n c n a) complement: 90∘ 75∘ 15∘ c n cn cn c n c n
b) supplement: 180∘ 89∘ 91∘ c n cn cn c n c n b) supplement: 180∘ 75∘ 105∘ c n cn cn c n c n
15. Since the angles with measures 4x∘ and 6x∘ are assumed to be complemen
c n cn cn cn cn cn c n c n cn cn cn cn cn
tary, we know that 4x∘ 6x∘ 90∘. Simplifying this yields
cn cn cn cn cn cn cn cn c n cn cn
10x∘ 90∘, cn cn cn c n so that x 9. So, the two angles have measures 36∘and 54∘ .
cn c n cn cn c n cn cn cn cn cn c n cn cn
16. Since the angles with measures 3x∘ and 15x∘ are assumed to be supplemen
c n cn cn cn cn cn c n c n cn cn cn cn cn
tary, we know that 3x∘ 15x∘ 180∘. Simplifying this yields
cn cn cn cn cn cn cn cn c n cn cn
18x∘ 180∘, so that cn cn cn cn cn x 10. So, the two angles have measures 30∘ and 150∘ .
cn cn c n cn cn cn cn cn c n cn cn cn
17. Since the angles with measures 8x∘ and
c n cn cn cn cn c n cn c n 4x∘ are assumed to be supplementa cn cn cn cn cn
ry, we know that 8x∘ 4x∘ 180∘. Simplifying this yields
cn cn cn cn cn cn cn cn c n cn cn
12x∘ 180∘, cn cn c n so that x 15. So, the two angles have measures 60∘ and 120∘ .
cn cn cn cn c n cn cn cn cn cn c n cn cn cn
18. Since the angles with measures 3x 15∘and 10x 10∘are assumed to be co
c n cn cn cn cn c n cn cn c n cn cn cn cn cn cn
mplementary, we know that 3x 15∘ 10x 10∘ 90∘. Simplifying this yields cn cn cn cn cn cn cn cn cn cn c n cn cn
13x 25∘ 90∘, cn cn cn cn cn so that 13x∘ 65∘ and thus, x 5. So, the two angles have meas
cn cn cn cn c n cn c n cn cn c n cn cn cn cn cn
ures 30∘and 60∘ .
c n cn cn
19. Since 180∘, we know th
c n cn cn cn cn cn c n cn c n cn cn 20. Since 180∘, we know th
c n cn cn cn cn cn c n cn c n cn cn
at at
1 17∘ –33∘ 180∘ and so, 30∘ . 1 10∘ –45∘ 180∘ and so, 25∘ .
– –
cn cn cn cn cn cn cn c n cn cn cn cn cn cn cn cn cn cn cn cn cn cn
cn cn
cn150∘ cn155∘
21. Since 180∘, we know th
c n cn cn cn cn cn c n cn c n cn cn 22. Since 180∘, we know th
c n cn cn cn cn cn c n cn c n cn cn
at at
4 180∘ and so, 30∘.
cn cn cn cn cn cn cn cn cn cn cn cn cn 3 180∘ and so, 36∘.
cn cn cn cn cn cn cn cn cn cn cn cn cn
–– –– –– ––
cn6cn cn5
Thus, 4 120∘ and 30∘ .
c n cn cn c n cn c n cn c n cn c n cn cn Thus, 3 108∘ and 36∘ .
c n cn cn c n cn c n cn c n cn c n cn cn
3
,
