5. rri
Geometry 321
3.
The measures ofa pair ofvertical angles are represented by 5w
-
and Zto + 16. a. Find the value of each angle.
u'. b. Find the measure
Solution: Vertical an,gles are equal in
m,easure.
20
of
5w-20=2w't76 3ur-20:16 3ru : 36 tu=L2 5w - 20 = 5(12) - 20 : 60 2w + 16 : 2$2) + 16 = 24
*
20 : 40 16 = 40
Check:
Since each angle has a measure of40o, the vertical angles are equal
in
measure.
Answer: a, w
: 12 b. Each angle measures 40o.
EXERCISES
Complementary Angles
In 1-10, write the measure of the complement of the angle
whose
measure is given.
1. 40" 6. rno
2.
25"
7.
do
3. 45" 4.69.5" 8. (90 - y)" 9. (r + 10)"
5.
rri'
10. 6
-
20)'
In t1-14, zA
and, zB are complementary. Find the measure of each measures are represented by the given expressions. Solve the problem algebraically using an equation.
angle
iftheir
fl. mzA = tr,mzB :5x f3. mzA:r,[lzB:x-40
12. mzB:.r,mzA: r*50 14. mzB : y,mzA :2y + 30
In 15-19, solve the problem algebraically using an equation. 15. Two angles are complementary. One angle is twice as large as the other. Find the number of degrees in each angle. 16. The complement of an angle is 8 times as large as lhe angle, Find the measure of the complement.
17. The complement of an angle is one-fifth of the measure of the angle. Find the measure of the angle.
lntegrated Mathematlcs: Course
I
18. The complement of an irngle measures 20" more than the angle. Find the number of degreres in bhe angle. 19. Find the number r.rf degrecs in an tngle thart measures 8'' lerss than its complement.
In 44-46, A7& u"a F^i i 44. If m z RTM = Sr uncl ,{5. lf mzMTS = 4r 6,
-
-16.
Supplementary Angles
lf mzRTM : Zr t I
In 20-29, write the measure of the supplement of the angle whose measrlre is given.
20. 40' 25. mo
21. 69' 26. co
22. 90" 27. t2v)'
24. 167:" 110" 28, (180 - ,)' 29. (r i +ol'
2s.
In 30-33, zA and. zB form a linear pair. (They are supplementary.) Find the measure of each angle if their measures are represented by the given exprerssions. Solve the problem algebraically using an equa-
In 47-54, based on the angle named. 47. Giuen:tF mzEGI :
t
CE;
G2.
tion.
30. mzA : r, D zB : 32. tmzA .= u,, mzB :
3:r
ur
-
30
gt. mzB: J, m ,A : ly 33. mzB:-r,mzA:rf
EGI
80
Fincl: mzFGH: mzHt
In 3-1-37, solve the problem algebraically using an equation.
34. Two
angles are supplementary. The measure of one angle is twice as large as the measure of the other. Find the number of degrees in each angle. The measure of the supplement of an angle is 40" more than the measure of the angle. Find the number of degrees in the supplement. Find the ntrmber of deglees in the measure of an angle that is 20" less than 4 times the measure of its supplement. 37. The difference between the measures of two supplementary angles is 80'. Find the measul'e of the larger of the two angles.
Giuen: zGKH and are a linear pair;
zh
-+ KHLKJ:wzIK,I=,
38. The supplement of the complement of an acute angle is alrvays (1) an acute angle (2) a right angle t3) an obtuse angle i4) a straight angle
l'ertical ;lngles In 39-43,
iF
ancl
tE irrt"r.""t at E. Firrd the measure of angle BEC
r.vhen ungle AEID measures;
.i9.
:10 "
40.
65"
4t. 90'
Find: mz-HKI; zGKJ.
m
42. 12g.4" 43. fi,!'
'2,
mzIIK
Geometry
In 44-46, ffi
323
and F^i irrtu"*""t at T.
44, If mz RTM :5r and mzNTS : 3r + 10, find mzRTM. 45. lf mzMTS : 4.r - 60 and m zNTR : 2r, find mzMTS. 46. lf mzRTI[ : 7x + 16 zrnd m zNTS : 3x 'r 48, find mzN?S. Miscelianeous
In
47-54, based on the given conditions, find the measure of each
erngle named.
47.
3.
The measures ofa pair ofvertical angles are represented by 5w
-
and Zto + 16. a. Find the value of each angle.
u'. b. Find the measure
Solution: Vertical an,gles are equal in
m,easure.
20
of
5w-20=2w't76 3ur-20:16 3ru : 36 tu=L2 5w - 20 = 5(12) - 20 : 60 2w + 16 : 2$2) + 16 = 24
*
20 : 40 16 = 40
Check:
Since each angle has a measure of40o, the vertical angles are equal
in
measure.
Answer: a, w
: 12 b. Each angle measures 40o.
EXERCISES
Complementary Angles
In 1-10, write the measure of the complement of the angle
whose
measure is given.
1. 40" 6. rno
2.
25"
7.
do
3. 45" 4.69.5" 8. (90 - y)" 9. (r + 10)"
5.
rri'
10. 6
-
20)'
In t1-14, zA
and, zB are complementary. Find the measure of each measures are represented by the given expressions. Solve the problem algebraically using an equation.
angle
iftheir
fl. mzA = tr,mzB :5x f3. mzA:r,[lzB:x-40
12. mzB:.r,mzA: r*50 14. mzB : y,mzA :2y + 30
In 15-19, solve the problem algebraically using an equation. 15. Two angles are complementary. One angle is twice as large as the other. Find the number of degrees in each angle. 16. The complement of an angle is 8 times as large as lhe angle, Find the measure of the complement.
17. The complement of an angle is one-fifth of the measure of the angle. Find the measure of the angle.
lntegrated Mathematlcs: Course
I
18. The complement of an irngle measures 20" more than the angle. Find the number of degreres in bhe angle. 19. Find the number r.rf degrecs in an tngle thart measures 8'' lerss than its complement.
In 44-46, A7& u"a F^i i 44. If m z RTM = Sr uncl ,{5. lf mzMTS = 4r 6,
-
-16.
Supplementary Angles
lf mzRTM : Zr t I
In 20-29, write the measure of the supplement of the angle whose measrlre is given.
20. 40' 25. mo
21. 69' 26. co
22. 90" 27. t2v)'
24. 167:" 110" 28, (180 - ,)' 29. (r i +ol'
2s.
In 30-33, zA and. zB form a linear pair. (They are supplementary.) Find the measure of each angle if their measures are represented by the given exprerssions. Solve the problem algebraically using an equa-
In 47-54, based on the angle named. 47. Giuen:tF mzEGI :
t
CE;
G2.
tion.
30. mzA : r, D zB : 32. tmzA .= u,, mzB :
3:r
ur
-
30
gt. mzB: J, m ,A : ly 33. mzB:-r,mzA:rf
EGI
80
Fincl: mzFGH: mzHt
In 3-1-37, solve the problem algebraically using an equation.
34. Two
angles are supplementary. The measure of one angle is twice as large as the measure of the other. Find the number of degrees in each angle. The measure of the supplement of an angle is 40" more than the measure of the angle. Find the number of degrees in the supplement. Find the ntrmber of deglees in the measure of an angle that is 20" less than 4 times the measure of its supplement. 37. The difference between the measures of two supplementary angles is 80'. Find the measul'e of the larger of the two angles.
Giuen: zGKH and are a linear pair;
zh
-+ KHLKJ:wzIK,I=,
38. The supplement of the complement of an acute angle is alrvays (1) an acute angle (2) a right angle t3) an obtuse angle i4) a straight angle
l'ertical ;lngles In 39-43,
iF
ancl
tE irrt"r.""t at E. Firrd the measure of angle BEC
r.vhen ungle AEID measures;
.i9.
:10 "
40.
65"
4t. 90'
Find: mz-HKI; zGKJ.
m
42. 12g.4" 43. fi,!'
'2,
mzIIK
Geometry
In 44-46, ffi
323
and F^i irrtu"*""t at T.
44, If mz RTM :5r and mzNTS : 3r + 10, find mzRTM. 45. lf mzMTS : 4.r - 60 and m zNTR : 2r, find mzMTS. 46. lf mzRTI[ : 7x + 16 zrnd m zNTS : 3x 'r 48, find mzN?S. Miscelianeous
In
47-54, based on the given conditions, find the measure of each
erngle named.
47.
