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

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

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

### 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,  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 180° angle as 90°+30°+60°, so the addition sentence is 90°+30°+60°= 180°. And in the second image, we have constructed three points A, B, C, and formed a straight line we have divided 180° angle as 120°+60°, so the addition sentence is 120°+60°= 180°.

Question 2.
∠DEF = 90°

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

Explanation:

Here,  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 90° angle as 30°+60°, so the addition sentence is 30°+60°= 90°. And in the second image, we have constructed <DEF and we have divided 90° angle as 30°+60°, so the addition sentence is 30°+60°= 90°.

Question 3.
∠GHI = 120°

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

Explanation:

Here,  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 120° angle as 30°+90°, so the addition sentence is 30°+90°= 120°. And in the second image, we have constructed <GHI and we have divided 90° angle as 60°+60°, so the addition sentence is 60°+60°= 120°.

Question 4.
x° = 270°

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

Explanation:

Here,  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 270° angle as 60°+90°+120°, so the addition sentence is 60°+90°+120°= 270°. And in the second image, we have constructed <LKJ and we have divided 270° angle as 60°+60°+30°+60°+60°, so the addition sentence is 60°+60°+30°+60°+60°= 270°.

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. y° = 120° + 90°
y° = 210°

b. z° = _____________
z° = _____________
z° = 60°+30°
z° = 90°

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

c. x° = _____________
x° = _____________