## Engage NY Eureka Math 4th Grade Module 4 Lesson 9 Answer Key

### Eureka Math Grade 4 Module 4 Lesson 9 Problem Set Answer Key

Question 1.
Complete the table.

Refer to the below table.

Explanation:

In pattern block A, the total number that fit around one vertex is 4 and the interior angle measurement is 360Â° Ã· 4 which is 90Â° and the sum of the angles around the vertex is 90Â°+90Â°+90Â°+90Â°= 360Â°.
In pattern block B, the total number that fit around one vertex is 6 and the interior angle measurement is 360Â° Ã· 6 which is 60Â° and the sum of the angles around the vertex is 60Â°+60Â°+60Â°+60Â°+60Â°+60Â°= 360Â°.
In pattern block C, the total number that fit around one vertex is 3 and the interior angle measurement is 360Â° Ã· 3 which is 120Â° and the sum of the angles around the vertex is 120Â°+120Â°+120Â°= 360Â°.
In pattern block D, the total number that fit around one vertex is 6 and the interior angle measurement is 360Â° Ã· 6 which is 60Â° and the sum of the angles around the vertex is 60Â°+60Â°+60Â°+60Â°+60Â°+60Â°= 360Â°.
In pattern block E, the total number that fit around one vertex is 3 and the interior angle measurement is 360Â° Ã· 3 which is 120Â° and the sum of the angles around the vertex is 120Â°+120Â°+120Â°= 360Â°.
In pattern block F, the total number that fit around one vertex is 12 and the interior angle measurement is 360Â° Ã· 12 which is 30Â° and the sum of the angles around the vertex is 30Â°+30Â°+30Â°+30Â°+30Â°+30Â°+30Â°+30Â°+30Â°+30Â°+30Â°+30Â°= 360Â°.

Question 2.
Find the measurements of the angles indicated by the arcs.

Refer to the below table.

Explanation:

In pattern block A, the total number angle measurement which 150Â° and the sum of the angles around the vertex is 60Â°+90Â° which is 150Â°.
In pattern block B, the total number angle measurement which 180Â° and the sum of the angles around the vertex is 60Â°+120Â° which is 180Â°.
In pattern block C, the total number angle measurement which 210Â°, and the sum of the angles around the vertex is 120Â°+90Â° which is 210Â°.

Question 3.
Use two or more pattern blocks to figure out the measurements of the angles indicated by the arcs.

Refer to the below table.

Explanation:

In pattern block A, the total number angle measurement which 60Â°, and the sum of the angles around the vertex is 30Â°+30Â° which is 60Â°.
In pattern block B, the total number angle measurement which 210Â°, and the sum of the angles around the vertex is 120Â°+90Â° which is 210Â°.
In pattern block C, the total number angle measurement which 120Â°, and the sum of the angles around the vertex is 90Â°+30Â° which is 120Â°.

### Eureka Math Grade 4 Module 4 Lesson 9 Exit Ticket Answer Key

Question 1.
Describe and sketch two combinations of the blue rhombus pattern block that create a straight angle.
Refer to the below image.

Explanation:

Here, we have constructed two combinations of the blue rhombus pattern block that create a straight angle.

Question 2.
Describe and sketch two combinations of the green triangle and yellow hexagon pattern block that create a straight angle.
Refer to the below image.

Explanation:

Here, we have constructed two combinations of the green triangle and yellow hexagon pattern block that create a straight angle.

### Eureka Math Grade 4 Module 4 Lesson 9 Homework Answer Key

Sketch two different ways to compose the given angles using two or more pattern blocks. Write an addition sentence to show how you composed the given angle.

Question 1.
point A, B, and C form a straight line.

Refer to the below image.

Explanation:

Here,Â  we have constructed three points A, B, C, and formed a straight line, and formed two different ways to compose the given angles using two or more pattern blocks. In the first image, we have divided 180Â° angle as 90Â°+30Â°+60Â°, so the addition sentence is 90Â°+30Â°+60Â°= 180Â°. And in the second image, we have constructed three points A, B, C, and formed a straight line we have divided 180Â° angle as 120Â°+60Â°, so the addition sentence is 120Â°+60Â°= 180Â°.

Question 2.
âˆ DEF = 90Â°

The addition sentence is 30Â°+60Â°= 90Â°.

Explanation:

Here,Â  we have constructed <DEF a and formed two different ways to compose the given angles using two or more pattern blocks. In the first image, we have divided 90Â° angle as 30Â°+60Â°, so the addition sentence is 30Â°+60Â°= 90Â°. And in the second image, we have constructed <DEF and we have divided 90Â° angle as 30Â°+60Â°, so the addition sentence is 30Â°+60Â°= 90Â°.

Question 3.
âˆ GHI = 120Â°

The addition sentence for the <GHI is 30Â°+90Â°= 120Â°.
The addition sentence for the <GHI is 30Â°+90Â°= 120Â°

Explanation:

Here,Â  we have constructed <GHI a and formed two different ways to compose the given angles using two or more pattern blocks. In the first image, we have divided 120Â° angle as 30Â°+90Â°, so the addition sentence is 30Â°+90Â°= 120Â°. And in the second image, we have constructed <GHI and we have divided 90Â° angle as 60Â°+60Â°, so the addition sentence is 60Â°+60Â°= 120Â°.

Question 4.
xÂ° = 270Â°

The addition sentence for the first image is 60Â°+90Â°+120Â°= 270Â°.
The addition sentence for the second image is 60Â°+60Â°+30Â°+60Â°+60Â°= 270Â°.

Explanation:

Here,Â  we have constructed <LKJ a and formed two different ways to compose the given angles using two or more pattern blocks. In the first image, we have divided 270Â° angle as 60Â°+90Â°+120Â°, so the addition sentence is 60Â°+90Â°+120Â°= 270Â°. And in the second image, we have constructed <LKJ and we have divided 270Â° angle as 60Â°+60Â°+30Â°+60Â°+60Â°, so the addition sentence is 60Â°+60Â°+30Â°+60Â°+60Â°= 270Â°.

Question 5.
Micah built the following shape with his pattern blocks. Write an addition sentence for each angle indicated by an arc and solve. The first one is done for you.

a. yÂ° = 120Â° + 90Â°
yÂ° = 210Â°

b. zÂ° = _____________
zÂ° = _____________
zÂ° = 60Â°+30Â°
zÂ° = 90Â°

Explanation:
Here, the value of z is 60Â°+30Â° which is 90Â°

c. xÂ° = _____________
xÂ° = _____________