## Engage NY Eureka Math Grade 6 Module 4 Lesson 30 Answer Key

### Eureka Math Grade 6 Module 4 Lesson 30 Opening Exercise Answer Key

Opening Exercise:

Draw an example of each term, and write a brief description.

Acute:
Less than 90° Obtuse
Between 90° and 180° Right
Exactly 90° Straight
Exactly 180° Reflex
Between 180° and 360° ### Eureka Math Grade 6 Module 4 Lesson 30 Example Answer Key

Example 1:

∠ABC measures 90°. The angle has been separated into two angles. If one angle measures 57°, what is the measure of the other angle? In this lesson, we will be using algebra to help us determine unknown measures of angles.

How are these two angles related?
x° + 57° = 90°

What equation could we use to solve for x?
Now, let’s solve.
x° + 57° – 57° = 90° – 57°
x° = 33°
The measure of the unknown angle is 33°.

Example 2:

Michelle is designing a parking lot. She has determined that one of the angles should be 115°. What is the measure of angle x and angle y? How is angle x related to the 115° angle?
The two angles form o straight line. Therefore, they should add up to 180°.

What equation would we use to show this?
x° + 115° = 180°

How would you solve this equation?
115° was added to angle x, so I will take away 115° to get back to angle X.
x° + 115° – 115° = 180° – 115°
x° = 65°
The angle next to 115°, labeled with an x, is equal to 65°.

How is angle y related to the angle that measures 115°?
These two angles also form a straight line and must add up to 180°.
Therefore, angles x and y must both be equal to 65°.

Example 3:

A beam of light is reflected off a mirror. Below is a diagram of the reflected beam. Determine the missing angle measure. How are the angles in this question-related?
There are three angles that, when all placed together, form a straight line. This means that the three angles have a sum of 180°.

What equation could we write to represent the situation?
55° + x + 55° = 180°

How would you solve an equation like this?
We can combine the two angles that we do know.
55° + 550 + x° = 180°
110° + x° = 180°
110° – 110° + x° = 180° – 110°
x° = 70°
The angle of the bounce is 70°.

Example 4:

∠ABC measures 90°. It has been split into two angles, ∠ABD and ∠DBC. The measure of ∠ABD and ∠DBC is in a ratio of 4: 1. What are the measures of each angle? Use a tape diagram to represent the ratio 4: 1. What is the measure of each angle?
5 units = 90°
1 unit = 18°
4 units = 72°
∠ABD is 72°. ∠DBC is 18°

How can we represent this situation with an equation?
4x° + x° = 90°

Solve the equation to determine the measure of each angle.
4x° + x° = 90°
5x° = 90°
5x° ÷ 5 = 90° ÷ 5
x° = 18°
4x° = 4(18°) = 72°
The measure of ∠DBC is 18° and the measure of ∠ABD is 72°.

### Eureka Math Grade 6 Module 4 Lesson 30 Exercise Answer Key

Exercises:

Write and solve an equation in each of the problems.

Exercise 1.
∠ABC measures 900. It has been split into two angles, ∠ABD and ∠DBC. The measure of the two angles is in a ratio of 2: 1. What are the measures of each angle? x° + 2x° = 90°
3x° = 90°
$$\frac{3 x^{\circ}}{3}=\frac{90^{\circ}}{3}$$
x° = 30°
One of the angles measures 30°, and the other measures 60°.

Exercise 2.
Solve for x. x° + 64° + 37° = 180°
x° + 101° = 180°
x° + 101° – 101° = 180° – 101°
x° = 79°

Exercise 3.
Candice is building a rectangular piece of a fence according to the plans her boss gave her. One of the angles is not labeled. Write an equation, and use it to determine the measure of the unknown angle. x° + 49° = 90°
x° + 49° – 49° = 90° – 49°
x° = 41°

Exercise 4.
Rashid hit a hockey puck against the wall at a 38° angle. The puck hit the wall and traveled in a new direction. Determine the missing angle in the diagram. 38° + x° + 38° = 180°
76° + x° = 180°
76° – 76° + x° = 180° – 76°
x° = 104°
The measure of the missing angle is 104°.

Exercise 5.
Jaxon is creating a mosaic design on a rectangular table. He has added two pieces to one of the corners. The first piece has an angle measuring 38° and is placed in the corner. A second piece has an angle measuring 27° and is also placed in the comer. Draw a diagram to model the situation. Then, write an equation, and use it to determine the measure of the unknown angle in a third piece that could be added to the corner of the table. x° + 38° + 27° = 90°
x° + 65° = 90°
x° + 65° – 65° = 90° – 65°
x° = 25°
The measure of the unknown angle is 25°.

### Eureka Math Grade 6 Module 4 Lesson 30 Problem Set Answer Key

Write and solve an equation for each problem.

Question 1.
Solve for x. x° + 52° = 90°
x° + 52° – 52° = 90° – 52°
x° = 38°
The measure of the missing angle is 38°

Question 2.
∠BAE measures 90°. Solve for x. 15° + x + 25° = 90°
15° + 25° + x = 90
40° + x = 90°
40° – 40° + x = 90°
x° = 50°

Question 3.
Thomas is putting in a tile floor. He needs to determine the angles that should be cut in the tiles to fit in the comer. The angle in the comer measures 90°. One piece of the tile will have a measure of 24°. Write an equation, and use it to determine the measure of the unknown angle.
x° + 24° = 90°
x° + 24° – 24° = 90° – 24°
x° = 66°
The measure of the unknown angle is 66°.

Question 4.
Solve for x°. x° + 105° + 62° = 180°
x° + 167° = 180°
x° + 167° – 167° = 180° – 167°
x° = 13°
The measure of the missing angle is 13°.

Question 5.
Aram has been studying the mathematics behind pinball machines. He made the following diagram of one of his 52° + x° + 68° = 180°
120° + x° = 180°
120° + x° – 120° = 180° – 120°
x° = 60°
The measure of the missing angle is 60°.

Question 6.
The measures of two angles have a sum of 90°. The measures of the angles are in a ratio of 2: 1. Determine the measures of both angles.
2x° + x° = 90°
3x° = 90°
$$\frac{3 x^{\circ}}{3}=\frac{90^{\circ}}{3}$$
x° = 30°
The angles measure 30° and 60°.

Question 7.
The measures of two angles have a sum of 1800. The measures of the angles are in a ratio of 5: 1. Determine the measures of both angles.
5x° + x° = 180°
6x° = 180°
$$\frac{6 x^{\circ}}{6}=\frac{180}{6}$$
x° = 30°
The angles measure 30° and 150°.

### Eureka Math Grade 6 Module 4 Lesson 30 Exit Ticket Answer Key

Write an equation, and solve for the missing angle in each question.

Question 1.
Alejandro is repairing a stained glass window. He needs to take ft apart to repair ft. Before taking ft apart, he makes a sketch with angle measures to put ft back together. Write an equation, and use ft to determine the measure of the unknown angle. 40° + x° + 30° = 180°
x° + 40° + 30° = 180°
x° + 70° = 180°
x° + 70° – 70° = 180° – 70°
x° = 110°
The missing angle measures 110°.

Question 2.
Hannah is putting in a tile floor. She needs to determine the angles that should be cut in the tiles to fit in the corner. The angle in the comer measures 90°. One piece of the tile will have a measure of 38°. Wrfte an equation, and use it to determine the measure of the unknown angle. x° + 38° = 90°
38° – 38° = 90° – 38°
x° = 52°
The measure of the unknown angle is 52°.

### Eureka Math Grade 6 Module 4 Lesson 30 Subtraction of Decimals Answer Key

Subtraction of Decimals – Round 1:

Directions: Evaluate each expression.  Question 1.
55 – 50
5

Question 2.
55 – 5
50

Question 3.
5.5 – 5
0.5

Question 4.
5.5 – 0.5
5.0

Question 5.
88 – 80
8

Question 6.
88 – 8
80

Question 7.
8.8 – 8
0.8

Question 8.
8.8 – 0.8
8

Question 9.
33 – 30
3

Question 10.
33 – 3
30

Question 11.
3.3 – 3
0.3

Question 12.
1 – 0.3
0.7

Question 13.
1 – 0.03
0.97

Question 14.
1 – 0.003
0.997

Question 15.
0.1 – 0.03
0.07

Question 16.
4 – 0.8
3.2

Question 17.
4 – 0.08
3.92

Question 18.
4 – 0.008
3.992

Question 19.
0.4 – 0.08
0.32

Question 20.
9 – 0.4
8.6

Question 21.
9 – 0.04
8.96

Question 22.
9 – 0.004
8.996

Question 23.
9.9 – 5
4.9

Question 24.
9.9 – 0.5
9.4

Question 25.
0.99 – 0.5
0.49

Question 26.
0.99 – 0.05
0.94

Question 27.
4.7-2

Question 28.
4.7 – 0.2
4.5

Question 29.
0.47 – 0.2
0.27

Question 30.
0.47 – 0.02
0.45

Question 31.
8.4 – 1
7.4

Question 32.
8.4 – 0.1
8.3

Question 33.
0.84 – 0.1
0.83

Question 34.
7.2 – 5
5.2

Question 35.
7.2 – 0.5
6.7

Question 36.
0.72 – 0.5
0.22

Question 37.
0.72 – 0.05
0.67

Question 38.
8.6 – 7
1.6

Question 39.
8.6 – 0.7
7.9

Question 40.
0.86 – 0.7
0.16

Question 41.
0.86 – 0.07
0.79

Question 42.
5.1 – 4
1.1

Question 43.
5.1 – 4.7
0.4

Question 44.
0.51 – 0.4
0.11

Subtraction of Decimals-Round 2:

Directions: Evaluate each expression:  Question 1.
66 – 60
6

Question 2.
66 – 6
60

Question 3.
6.6 – 6
0.6

Question 4.
6.6 – 0.6
6

Question 5.
99 – 90
9

Question 6.
99 – 9
90

Question 7.
9.9 – 9
0.9

Question 8.
9.9 – 0.9
9

Question 9.
22 – 20
2

Question 10.
22 – 2
20

Question 11.
2.2 – 2
0.2

Question 12.
3 – 0.4
2.6

Question 13.
3 – 0.04
2.96

Question 14.
3 – 0.004
2.996

Question 15.
0.3 – 0.04
0.26

Question 16.
8 – 0.2
7.8

Question 17.
8 – 0.02
7.98

Question 18.
8 – 0.002
7.998

Question 19.
0.8 – 0.02
0.78

Question 20.
5 – 0.1
4.9

Question 21.
5 – 0.01
4.99

Question 22.
5 – 0.001
4.999

Question 23.
6.8 – 4
2.8

Question 24.
6.8 – 0.4
6.4

Question 25.
0.68 – 0.4
0.28

Question 26.
0.68 – 0.04
0.64

Question 27.
7.3 – 1
6.3

Question 28.
7.3 – 0.1
7.2

Question 29.
0.73 – 0.1
0.63

Question 30.
0.73 – 0.01
0.72

Question 31.
9.5 – 2
7.5

Question 32.
9.5 – 0.2
9.3

Question 33.
0.95 – 0.2
0.75

Question 34.
8.3 – 5
3.3

Question 35.
8.3 – 0.5
7.8

Question 36.
0.83 – 0.5
0.33

Question 37.
0.83 – 0.05
0.78

Question 38.
7.2 – 4
3.2

Question 39.
7.2 – 0.4
6.8

Question 40.
0.72 – 0.4
0.32

Question 41.
0.72 – 0.04
0.68

Question 42.
9.3 – 7