## 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:

Answer:

Less than 90Â°

Obtuse

Answer:

Between 90Â° and 180Â°

Right

Answer:

Exactly 90Â°

Straight

Answer:

Exactly 180Â°

Reflex

Answer:

Between 180Â° and 360Â°

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

Example 1:

âˆ ABC measures 90Â°. The angle has been separated into two angles. If one angle measures 57Â°, what is the measure of the other angle?

Answer:

In this lesson, we will be using algebra to help us determine unknown measures of angles.

How are these two angles related?

Answer:

xÂ° + 57Â° = 90Â°

What equation could we use to solve for x?

Answer:

Now, letâ€™s solve.

xÂ° + 57Â° – 57Â° = 90Â° – 57Â°

xÂ° = 33Â°

The measure of the unknown angle is 33Â°.

Example 2:

Michelle is designing a parking lot. She has determined that one of the angles should be 115Â°. What is the measure of angle x and angle y?

How is angle x related to the 115Â° angle?

Answer:

The two angles form o straight line. Therefore, they should add up to 180Â°.

What equation would we use to show this?

Answer:

xÂ° + 115Â° = 180Â°

How would you solve this equation?

Answer:

115Â° was added to angle x, so I will take away 115Â° to get back to angle X.

xÂ° + 115Â° – 115Â° = 180Â° – 115Â°

xÂ° = 65Â°

The angle next to 115Â°, labeled with an x, is equal to 65Â°.

How is angle y related to the angle that measures 115Â°?

Answer:

These two angles also form a straight line and must add up to 180Â°.

Therefore, angles x and y must both be equal to 65Â°.

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?

Answer:

There are three angles that, when all placed together, form a straight line. This means that the three angles have a sum of 180Â°.

What equation could we write to represent the situation?

Answer:

55Â° + x + 55Â° = 180Â°

How would you solve an equation like this?

Answer:

We can combine the two angles that we do know.

55Â° + 550 + xÂ° = 180Â°

110Â° + xÂ° = 180Â°

110Â° – 110Â° + xÂ° = 180Â° – 110Â°

xÂ° = 70Â°

The angle of the bounce is 70Â°.

Example 4:

âˆ ABC measures 90Â°. It has been split into two angles, âˆ ABD and âˆ DBC. The measure of âˆ ABD and âˆ 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 = 90Â°

1 unit = 18Â°

4 units = 72Â°

âˆ ABD is 72Â°. âˆ DBC is 18Â°

How can we represent this situation with an equation?

Answer:

4xÂ° + xÂ° = 90Â°

Solve the equation to determine the measure of each angle.

4xÂ° + xÂ° = 90Â°

5xÂ° = 90Â°

5xÂ° Ã· 5 = 90Â° Ã· 5

xÂ° = 18Â°

4xÂ° = 4(18Â°) = 72Â°

The measure of âˆ DBC is 18Â° and the measure of âˆ ABD is 72Â°.

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

Exercises:

Write and solve an equation in each of the problems.

Exercise 1.

âˆ ABC measures 900. It has been split into two angles, âˆ ABD and âˆ DBC. The measure of the two angles is in a ratio of 2: 1. What are the measures of each angle?

Answer:

xÂ° + 2xÂ° = 90Â°

3xÂ° = 90Â°

\(\frac{3 x^{\circ}}{3}=\frac{90^{\circ}}{3}\)

xÂ° = 30Â°

One of the angles measures 30Â°, and the other measures 60Â°.

Exercise 2.

Solve for x.

Answer:

xÂ° + 64Â° + 37Â° = 180Â°

xÂ° + 101Â° = 180Â°

xÂ° + 101Â° – 101Â° = 180Â° – 101Â°

xÂ° = 79Â°

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.

Answer:

xÂ° + 49Â° = 90Â°

xÂ° + 49Â° – 49Â° = 90Â° – 49Â°

xÂ° = 41Â°

Exercise 4.

Rashid hit a hockey puck against the wall at a 38Â° angle. The puck hit the wall and traveled in a new direction. Determine the missing angle in the diagram.

Answer:

38Â° + xÂ° + 38Â° = 180Â°

76Â° + xÂ° = 180Â°

76Â° – 76Â° + xÂ° = 180Â° – 76Â°

xÂ° = 104Â°

The measure of the missing angle is 104Â°.

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 38Â° and is placed in the corner. A second piece has an angle measuring 27Â° 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.

Answer:

xÂ° + 38Â° + 27Â° = 90Â°

xÂ° + 65Â° = 90Â°

xÂ° + 65Â° – 65Â° = 90Â° – 65Â°

xÂ° = 25Â°

The measure of the unknown angle is 25Â°.

### 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.

Answer:

xÂ° + 52Â° = 90Â°

xÂ° + 52Â° – 52Â° = 90Â° – 52Â°

xÂ° = 38Â°

The measure of the missing angle is 38Â°

Question 2.

âˆ BAE measures 90Â°. Solve for x.

Answer:

15Â° + x + 25Â° = 90Â°

15Â° + 25Â° + x = 90

40Â° + x = 90Â°

40Â° – 40Â° + x = 90Â°

xÂ° = 50Â°

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 90Â°. One piece of the tile will have a measure of 24Â°. Write an equation, and use it to determine the measure of the unknown angle.

Answer:

xÂ° + 24Â° = 90Â°

xÂ° + 24Â° – 24Â° = 90Â° – 24Â°

xÂ° = 66Â°

The measure of the unknown angle is 66Â°.

Question 4.

Solve for xÂ°.

Answer:

xÂ° + 105Â° + 62Â° = 180Â°

xÂ° + 167Â° = 180Â°

xÂ° + 167Â° – 167Â° = 180Â° – 167Â°

xÂ° = 13Â°

The measure of the missing angle is 13Â°.

Question 5.

Aram has been studying the mathematics behind pinball machines. He made the following diagram of one of his

Answer:

52Â° + xÂ° + 68Â° = 180Â°

120Â° + xÂ° = 180Â°

120Â° + xÂ° – 120Â° = 180Â° – 120Â°

xÂ° = 60Â°

The measure of the missing angle is 60Â°.

Question 6.

The measures of two angles have a sum of 90Â°. The measures of the angles are in a ratio of 2: 1. Determine the measures of both angles.

Answer:

2xÂ° + xÂ° = 90Â°

3xÂ° = 90Â°

\(\frac{3 x^{\circ}}{3}=\frac{90^{\circ}}{3}\)

xÂ° = 30Â°

The angles measure 30Â° and 60Â°.

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.

Answer:

5xÂ° + xÂ° = 180Â°

6xÂ° = 180Â°

\(\frac{6 x^{\circ}}{6}=\frac{180}{6}\)

xÂ° = 30Â°

The angles measure 30Â° and 150Â°.

### 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.

Answer:

40Â° + xÂ° + 30Â° = 180Â°

xÂ° + 40Â° + 30Â° = 180Â°

xÂ° + 70Â° = 180Â°

xÂ° + 70Â° – 70Â° = 180Â° – 70Â°

xÂ° = 110Â°

The missing angle measures 110Â°.

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 90Â°. One piece of the tile will have a measure of 38Â°. Wrfte an equation, and use it to determine the measure of the unknown angle.

Answer:

xÂ° + 38Â° = 90Â°

38Â° – 38Â° = 90Â° – 38Â°

xÂ° = 52Â°

The measure of the unknown angle is 52Â°.

### 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

Answer:

5

Question 2.

55 – 5

Answer:

50

Question 3.

5.5 – 5

Answer:

0.5

Question 4.

5.5 – 0.5

Answer:

5.0

Question 5.

88 – 80

Answer:

8

Question 6.

88 – 8

Answer:

80

Question 7.

8.8 – 8

Answer:

0.8

Question 8.

8.8 – 0.8

Answer:

8

Question 9.

33 – 30

Answer:

3

Question 10.

33 – 3

Answer:

30

Question 11.

3.3 – 3

Answer:

0.3

Question 12.

1 – 0.3

Answer:

0.7

Question 13.

1 – 0.03

Answer:

0.97

Question 14.

1 – 0.003

Answer:

0.997

Question 15.

0.1 – 0.03

Answer:

0.07

Question 16.

4 – 0.8

Answer:

3.2

Question 17.

4 – 0.08

Answer:

3.92

Question 18.

4 – 0.008

Answer:

3.992

Question 19.

0.4 – 0.08

Answer:

0.32

Question 20.

9 – 0.4

Answer:

8.6

Question 21.

9 – 0.04

Answer:

8.96

Question 22.

9 – 0.004

Answer:

8.996

Question 23.

9.9 – 5

Answer:

4.9

Question 24.

9.9 – 0.5

Answer:

9.4

Question 25.

0.99 – 0.5

Answer:

0.49

Question 26.

0.99 – 0.05

Answer:

0.94

Question 27.

4.7-2

Answer:

Question 28.

4.7 – 0.2

Answer:

4.5

Question 29.

0.47 – 0.2

Answer:

0.27

Question 30.

0.47 – 0.02

Answer:

0.45

Question 31.

8.4 – 1

Answer:

7.4

Question 32.

8.4 – 0.1

Answer:

8.3

Question 33.

0.84 – 0.1

Answer:

0.83

Question 34.

7.2 – 5

Answer:

5.2

Question 35.

7.2 – 0.5

Answer:

6.7

Question 36.

0.72 – 0.5

Answer:

0.22

Question 37.

0.72 – 0.05

Answer:

0.67

Question 38.

8.6 – 7

Answer:

1.6

Question 39.

8.6 – 0.7

Answer:

7.9

Question 40.

0.86 – 0.7

Answer:

0.16

Question 41.

0.86 – 0.07

Answer:

0.79

Question 42.

5.1 – 4

Answer:

1.1

Question 43.

5.1 – 4.7

0.4

Answer:

Question 44.

0.51 – 0.4

Answer:

0.11

Subtraction of Decimals-Round 2:

Directions: Evaluate each expression:

Question 1.

66 – 60

Answer:

6

Question 2.

66 – 6

Answer:

60

Question 3.

6.6 – 6

Answer:

0.6

Question 4.

6.6 – 0.6

Answer:

6

Question 5.

99 – 90

Answer:

9

Question 6.

99 – 9

Answer:

90

Question 7.

9.9 – 9

Answer:

0.9

Question 8.

9.9 – 0.9

Answer:

9

Question 9.

22 – 20

Answer:

2

Question 10.

22 – 2

Answer:

20

Question 11.

2.2 – 2

Answer:

0.2

Question 12.

3 – 0.4

Answer:

2.6

Question 13.

3 – 0.04

Answer:

2.96

Question 14.

3 – 0.004

Answer:

2.996

Question 15.

0.3 – 0.04

Answer:

0.26

Question 16.

8 – 0.2

Answer:

7.8

Question 17.

8 – 0.02

Answer:

7.98

Question 18.

8 – 0.002

Answer:

7.998

Question 19.

0.8 – 0.02

Answer:

0.78

Question 20.

5 – 0.1

Answer:

4.9

Question 21.

5 – 0.01

Answer:

4.99

Question 22.

5 – 0.001

Answer:

4.999

Question 23.

6.8 – 4

Answer:

2.8

Question 24.

6.8 – 0.4

Answer:

6.4

Question 25.

0.68 – 0.4

Answer:

0.28

Question 26.

0.68 – 0.04

Answer:

0.64

Question 27.

7.3 – 1

Answer:

6.3

Question 28.

7.3 – 0.1

Answer:

7.2

Question 29.

0.73 – 0.1

Answer:

0.63

Question 30.

0.73 – 0.01

Answer:

0.72

Question 31.

9.5 – 2

Answer:

7.5

Question 32.

9.5 – 0.2

Answer:

9.3

Question 33.

0.95 – 0.2

Answer:

0.75

Question 34.

8.3 – 5

Answer:

3.3

Question 35.

8.3 – 0.5

Answer:

7.8

Question 36.

0.83 – 0.5

Answer:

0.33

Question 37.

0.83 – 0.05

Answer:

0.78

Question 38.

7.2 – 4

Answer:

3.2

Question 39.

7.2 – 0.4

Answer:

6.8

Question 40.

0.72 – 0.4

Answer:

0.32

Question 41.

0.72 – 0.04

Answer:

0.68

Question 42.

9.3 – 7

Answer:

2.3

Question 43.

9.3 – 0.7

Answer:

8.6

Question 44.

0.93 – 0.7

Answer:

0.23