Local District South
Getting Smarter and More Balanced
Mathematics 7
Week 3 Take Home Packet
________________________________________________
SCHOOL
Student Name
________________________________________________
Teacher: __________________________________
Period :______
2
GETTING SMARTER AND MORE BALANCED
MATHEMATICS 7 – Week 3 - DAY 1
GEOMETRY: Angle Relationships
A
An angle measures the amount of turn between
two lines around their common point (the vertex).
Angles are measured in degrees. We use a protractor
to measure angles.
B
vertex
C
Angles are named using the angle symbol () , the vertex point, and a point on each of the angle's rays.
The name of the angle is simply the three letters representing those points, with the vertex point listed in
the middle. The angle above may be named ABC or CBA.
Below are four types of angles based on their angle measure.
A square is used to
Identify a right angle.
YOUR TURN. Name the angles below using the  symbol and then write the type of angle based on
the angle’s measure.
Remember that the vertex has to be the middle point.
 ABC
____________
____________
____________
____________
____________
____________
____________
acute angle
____________
3
Have you heard about complimentary and supplementary angles?
Let’s use what we learned to find the missing angles below.
 ABD
: I know that the two angles add up to 90°.
I can solve this in two ways.
ABD + 24 = 90
- 24 -24
ABD
= 66°
or
ABD = 90 – 24
= 66°
Let’s check:
66 + 24 = 90
Find the measure of  DBC
:I know that the two angles add up to 180°
because they are supplementary.
138 + DBC = 180
-138
-138
DBC = 42°
or
Let’s check:
138 + 42 = 180
DBC = 180 – 138
= 42°
4
YOUR TURN. Identify each pair of angles as complementary, supplementary, or neither.
Remember that complementary angles add up to 90° or form a square corner while
supplementary angles add up to 180°.
Example:
30°
30°
😊 Complementary
45°
45°
Now let’s find the missing angles below.
5
GETTING SMARTER AND MORE BALANCED
MATHEMATICS 7 – Week 3 - DAY 2
GEOMETRY: More on Angle Relationships
A
Vertical Angles
B
Hmmm… Looking at the figure, I know
the following:
1. ACB and  DCE have the same measure.
And because they are opposite each other
they are vertical angles.
C
Adjacent Angles
D
E
2. ACD and  BCE should also have the
same measure because they are opposite
each other.
But wait, there’s more! I see that ACB and BCE are adjacent angles. They
share the same vertex C and the same side CB. And since ACB and BCE form a
straight angle, their measures add up to 180°.
55 + BCE = 180
-55
-55
BCE = 125°
Let’s try another one.
Using what we know about straight, complementary, supplementary, vertical and adjacent
angles, let’s find the measure of CDF, ADB and FDG.
➢ Look! CDF and BDF are vertical angles. That means they
both measure 70° because vertical angles measure the same.
CDF = 70°
➢ How do I find ADB ? (Shade ADB)
CDF is a straight angle and CDA + ADB + BDE = CDF.
Therefore, CDA + ADB + BDE = 180°
85° + ADB + 70° = 180°
ADB + 155° = 180°
-155° -155°
ADB
= 25°
➢ Now let’s find the measure of FDG. (Shade FDG)
CDE is a straight angle and CDF = 70°. We know that CDF + FDG + GDE = CDE.
CDF + FDG + GDE = 180°
70° + FDG + 50° = 180°
FDG + 120° = 180°
-120° -120°
FDG
= 60°
6
YOUR TURN. Using what we know about straight, complementary, supplementary, vertical and
adjacent angles.
Remember that vertical angles are equal, complementary angles adds up
to 90°, straight and supplementary angles measure 180°. If you need more help, go to the bit.ly below.
bit.ly/vertical-angles
II. Find the measure of each lettered angle. c and d were done for you.
a
b
d
c
c = 80°
The angle that measures 80°
is vertical to angle c.
Therefore, angle c is also 80°.
d = 100°
80° + d = 180
180 – 80 = 100
g
j
h
m
k
n
7
GETTING SMARTER AND MORE BALANCED
MATHEMATICS 7 – Week 3 - DAY 3
GEOMETRY: Putting It All Together
Let’s do some math.
Find the measures of two supplementary angles if the measure of one angle is
6 less than five times the measure of the other angle.
We know the sum of the measures of supplementary
angles is 180. Let’s draw two angles, A and B
with their measures.
Let’s x° be the measure of A and
6 less than five times the other angle or (5x-6) be the measure of B.
The angles are supplementary. Therefore, x + (5x – 6) = 180. Let’s solve for A and B.
First solve for x.
= 31°
✓ 31° + 149° = 180°
= 5(31) – 6
= 155 – 6
= 149°
8
YOUR TURN.
1. Find the measures of two complementary angles
if one angle measures six degrees less than five
times the measure of the other.
Remember:
Complementary angles adds up to 90°
2. Solve for x then find the measure of AOB and
BOC.
3. Solve for x then find the measure of AOB and
BOC.
4. Find the measure of BAC.
Remember that
vertical angels have the same measure.
B
A
C
5. Solve for x then find the measure of AOB and
BOC.
6. Lines XU and WY
intersect at point A.
Based on the diagram, select
True or False for each statement.
9
GETTING SMARTER AND MORE BALANCED
MATHEMATICS 7 – Week 3 - DAY 4
Did you know…
Let’s try it. Find the measure of A and B.
B
C = 56° (given)
A = x
= 31°
A
B = 3x
C
4
= 3(31°)
4
= 93°
YOUR TURN. Find the missing angles. Let’s call the angles x or y.
1.
2.
y + 51 + 62 = 180
y + 113 = 180
-113 -113
y = 67
y = 67°
x + y = 180
x + 67 = 180
- 67
-67
x = 113
x = 113°
3.
4.
10
Math Recall: Let’s revisit how to solve equations and inequalities.
Watch more examples on
bit.ly/solve-inequalities
YOUR TURN.
1. Solve for x. 5 x + 5 = 15
3. Javier’s fuel tank holds 12¾ gallons of gasoline
when completely full. He had some gas in the
tank and added 10¼ gallons of gasoline to fill it
completely.
How many gallons of gasoline were in the tank
before Javier added some?
Write an equation that models this situation.
2. Solve then graph the inequality 7x – 2 ≥ 12.
4. Which number line shows the solution to the
inequality
–3x – 5 < –2?
5. Solve for a and b.
11
6. Linda has $26. She wants to buy a ski pass for
$80. She can earn $6 per hour to babysit.
Write an inequality that represents the number of
hours (h) Linda could babysit to earn at least enough
money to buy the ski pass.
a
= b
What is the minimum number of hours Linda have to
babysit to have enough money?
7. A coach buys a uniform and a basketball for
each of the 15 players on the team. Each
basketball costs $9. The coach spends a total of
$420 for uniforms and basketballs.
8. David goes into a candy store with $5.00. He buys 9
peppermints for $0.15 each, and some sour candies.
Each sour candy costs $0.25.
Enter the cost, in dollars, of 1 uniform.
What is the maximum number of sour candies David
can buy?
Enter an equation that models the situation with u,
the cost of one uniform.
Write an inequality that can model this situation.
9. Can you find the error in Alyssa’s problem? If
so, explain and correct the error.
10. Below is Stacy’s HW. Can you find the error in her
problem? If so, explain and correct the error.
Explanation:
Explanation: