Warm Up:
1. Using the HW guide lines, grade your HW
-4 out of 4 is if you fully completed your homework
-3 out of 3 is if you did must of your work, but not fully completed
-2 out of 2 is if you completed your homework half way
-1 out of 1 is if you did a little bit of the homework
-0 out of is 0 is if you didn’t do any thing of your homework
-10% token off your grade work effort for every day its late
2.[6]=6
3.[-6]=6
4.[5-2]=3
5.[2-5]=3
-two and three are the same, and four and five are the same
6.Using the answer key, grade your HW
Homework: Pg. # 15-17, 25, 32-35
Pg.# 19
Reproduce all diagrams
PG. 29
15. m<MQV=90 m<VQP=35
What is m<MQP?
90 + 35=125
Explanation: its 125 because the
angle m<MQV is 90 degrees and
m<VQP is 35 degrees, so add
them to equals 125
16.m<MVQ=55 m<QVP=?
55 + _ = 180-is because together they make a straight
angle, or another name for it is a
supplementary angle.
m<QVP=180-55=125
Explanation: the answer is 125 because since the angle m<MQP is a
supplementary angle and equals 180, you are to subtract 55 from
180 to equal 125.
17. Judging by appearance, name each of the
following.
a. Two acute angles
b. Two obtuse angles
c. Two right angles
a. acute: <QPV & <MNP (or others)
b. obtuse: <MQP & <MNP (or others)
c. right: <MQV & <VNP (or others)
Explanation: the angles that are acute is
because they are angles whose measure is
between 0 and 90 degrees. The angles that
are obtuse is because they are angles whose
measure is between 90 and 180 degrees. The angles that are right is because they are angle
whose measure is 90 degrees. To tell if angle is right also is that it would have a box within the
angle. Right angles are also called complementary angles.
25. Open-ended Name two times when the hands of a clock
A. form an acute angle.
B. form a right angle.
C. form an obtuse angle.
D. form a straight angle.
A.
B.
C.
D.
12:oo & 1:00, 9:00 & 8:00
3:00 & 6:00, 2:00 & 5:00
11:00 & 4:00, 2:00 & 9:00
12:00 & 6:00, 10:00 & 5:00
-Can have other answers
32)m<AOC=7x-2, m<AOB=2x+8, m<BOC=3x+14
2x+8 +3x+4=7x-2
5x + 12 = 7x-2
-5x
-5x
12=2x-2
2x-2=12
+2 +2
2x=14
2 2
X=7
M<AOC=7(7)-2
M<AOB=2(7)+8
49-2
14+8
=47
=22
M<BOC=3(7)+14
21+14
35
35+22=47
Explanation: Well <AOB and <BOC equals <AOC, so add <AOC with <BOC to get <AOC. So then add like
terms or substitute 2x+3x=5x and then subtract 5x from 7x=2x. After doing that add 2 to 12=14. Then
divide 2 into 14 and get x=7. Once you do that, substitute 7 as for x in the equations of the angles and
then check.
33) m<AOB=4X-2, m<BOC=5X+10,m<COD=2x+14
4x-2=2x+14
-2x -2x
2x-2=14
+2 +2
2x=16
2 2
X=8
M<AOB=4(8)-2
32-2=30
M<COD=2(8)+14
16+14=30
30=30
Explanation: the reason you don’t use the equation from m<BOC is because it really doesn’t matter.
That is because you focus on m<AOC & m<COD cause they are congruent, you can tell that by the red or
pink lines that are marked a like for both of those angles. So add m<AOB and m<BOC cause they are
congruent from each other. So combine like terms, starting with subtracting 2x from 4x=2x. Then add 2
to 14=16, after that divide 2 into 16 and get x=8. Once you do that, substitute 8 as for x into the
equations of the angles and then check.
34)m<AOB=28, m<BOC=3x-2, m<AOD=6x
28+28+3x-2=6x
56+3x-2=6x
3x+54=6x
-3x
-3x
54=3x
3 3
x=18
m<BOC=3(18)-2
54-2
52
m<AOD=6(18)=108
28+28+52= 108
Explanation: the answer for x is 18 because to figure out <AOD you need to add 28+28+3x-2 to equal 6x.
You have another 28 to represent <COD because that angle is congruent with <AOB, which is 28. Add
those two angle with <BOC and get <AOD. So add the like terms first with 28+28+-2=54. Then subtract
3x from 6x=3x. After that divide 3 into 54 and get x=18. Once you do that, substitute 18 as for x into the
equations of the angles and then check.
35)m<AOB=4x+3, m<BOC=7x, m<AOD=16x-1
4x+3+4x+3+7x=16x-1
15x+6=16x-1
-15x -15x
x-1=6
+1 +1
X=7
m<A0B & <COD=4(7)+3
28+3=31
m<BOC=7(7)=49
m<AOD=16(7)-1
112-1=111
31+49=31=111
Explanation: x is 7 because to figure out m<AOD, you
need to add <AOB,<BOC,<COD together. First was to figure out what angle <COD equation which is 4x+3
because <COD is congruent to <AOB. First add like terms together-4x+4x+7x=15x and 3+3=6 equaling
15x+6=16x-1. Then subtract 15x from 16x=x-1=6. Add l to 6 and to get x=7. Once you got x, then
substitute x into the equations and then check your work.
PG. 648
19)m<ACD=60 AND m<DCH=20. Find m<HCA.
m<HCA=40 DEGREES
-so subtract 60-20 and get 40
Notes: