## Engage NY Eureka Math 4th Grade Module 4 Lesson 5 Answer Key

### Eureka Math Grade 4 Module 4 Lesson 5 Problem Set Answer Key

Question 1.
Make a list of the measures of the benchmark angles you drew, starting with Set A.
Round each angle measure to the nearest 5° Both sets have been started for you.
a. Set A: 45°, 90°,
The angles that are nearest to 5° will be 90°, 180°, 270°, 360°.

Explanation:
Here, the list of the angles in Set A is 45°, 90°, 135°, 180°, 225°, 270°, 315°, 360°, so here we need to round off the each angle which is nearest to 5° and the angles will be 90°, 180°, 270°, 360° are the angles which are nearest to 5°.

b. Set B: 30°,60°,
The angles that are nearest to 5° will be 90°, 180°, 270°, 360°.

Explanation:
Here, the list of the angles in Set A is 30°, 60°, 90°, 120°, 150°, 180°, 210°, 240°,  so here we need to round off the each angle which is nearest to 5° and the angles will be 90°, 180°, 270°, 360° are the angles which are nearest to 5°.

Question 2.
Circle any angle measures that appear on both lists. What do you notice about them?
We have noticed that they all are right angles and they all are quarter turns.

Explanation:
The angles that are cricled are 90°, 180°, 270°, 360°, and we have noticed that they all are right angles and they all are quarter turns.

Question 3.
List the angle measures from Problem 1 that are acute. Trace each angle with your finger as you say its measurement.
The angles are 30°, 45°, and 60°.

Explanation:
The angles that measures from problem 1 that are acute which we have traced is 30°, 45°, and 60°.

Question 4.
List the angle measures from Problem 1 that are obtuse. Trace each angle with your finger as you say its measurement.
The angles are 120°, 135°, and 150°.

Explanation:
The angles that measures from problem 1 that are acute which we have traced is 120°, 135°, and 150°.

Question 5.
We found out today that 1° is $$\frac{1}{360}$$ of a whole turn. It is 1 out of 360°. That means a 2° angle is $$\frac{2}{360}$$ of a whole turn. What fraction of a whole turn is each of the benchmark angles you listed in Problem 1?
The angles in the set A are $$\frac{45}{360}$$,$$\frac{90}{360}$$, $$\frac{135}{360}$$,$$\frac{180}{360}$$,$$\frac{225}{360}$$,$$\frac{270}{360}$$, $$\frac{315}{360}$$, $$\frac{360}{360}$$.
The angles in the set A are $$\frac{30}{360}$$,$$\frac{60}{360}$$, $$\frac{90}{360}$$,$$\frac{120}{360}$$,$$\frac{150}{360}$$,$$\frac{180}{360}$$, $$\frac{210}{360}$$, $$\frac{240}{360}$$, $$\frac{270}{360}$$, $$\frac{240}{360}$$, $$\frac{300}{360}$$, $$\frac{330}{360}$$, $$\frac{360}{360}$$.

Explanation:
The fraction of a whole turn is each of the benchmark angles that are listed in problem 1 set A is $$\frac{45}{360}$$,$$\frac{90}{360}$$, $$\frac{135}{360}$$,$$\frac{180}{360}$$,$$\frac{225}{360}$$,$$\frac{270}{360}$$, $$\frac{315}{360}$$, $$\frac{360}{360}$$.
The fraction of a whole turn is each of the benchmark angles that are listed in problem 1 set B is $$\frac{30}{360}$$,$$\frac{60}{360}$$, $$\frac{90}{360}$$,$$\frac{120}{360}$$,$$\frac{150}{360}$$,$$\frac{180}{360}$$, $$\frac{210}{360}$$, $$\frac{240}{360}$$, $$\frac{270}{360}$$, $$\frac{240}{360}$$, $$\frac{300}{360}$$, $$\frac{330}{360}$$, $$\frac{360}{360}$$.

Question 6.
How many 45° angles does it take to make a full turn?
It takes eight 45° angles to make a full turn.

Explanation:
As the circle has 360° for full turn and for 45° It takes eight 45° angles to make a full turn.

Question 7.
How many 30° angles does it take to make a full turn?
It takes twelve 45° angles to make a full turn.

Explanation:
As the circle has 360° for full turn and for 45° It takes twelve 45° angles to make a full turn.

Question 8.
If you didn’t have a protractor, how could you reconstruct a quarter of it from 0° to 90°?
Here, we could use two 45° angles or three 30° angles and we will put them together and we can make a right angle template.

### Eureka Math Grade 4 Module 4 Lesson 5 Exit Ticket Answer Key

Question 1.
How many right angles make a full turn?
It takes four right angles to make a full turn.

Explanation:
As the circle has 360° for full turn and four right angles It takes four right angles to make a full turn.

Question 2.
What is the measurement of a right angle?
The measurement of a right angle is 90° as the set of two lines intersect each other at 90° and they form a right angle. So the measurement of right angle is 90°.

Question 3.
What fraction of a full turn is 1°
As a full turn is 360°, so 1° of 360° written in the fraction as $$\frac{1}{360}$$.

Question 4.
Name at least four benchmark angle measurements.
The four benchmark angle measurements are 30°, 45°, 60°, 90°.

Explanation:
Here the benchmarks are defined as the standard or reference point against which something can be measured or compared. And benchmark numbers are the numbers against which other numbers or qualities can be estimated or compared. Here the four benchmark angle measurements are 30°, 45°, 60°, 90°.

### Eureka Math Grade 4 Module 4 Lesson 5 Homework Answer Key

Question 1.
Identify the measures of the following angles.
a.

The above angle is measured as 60°.

Explanation:
In the above image, we can see that the angle is 60° and is known as acute angle. As the angle measures less than 90°, so the above angle is measured as 60°.

b.

The above angle is measured as 130°.

Explanation:
In the above image, we can see that the angle is 130° and is known as obtuse angle. As the angle measures greater than 90°. So the above angle is measured as 130°.

c.

The above angle is measured as 315°.

Explanation:
In the above image, we can see that the angle is 315° and is known as reflex angle. As the angle measures greater than 180°. So the above angle is measured as 315°.

d.

The above angle is measured as 120°.

Explanation:
In the above image, we can see that the angle is 120° and is known as obtuse angle. As the angle measures greater than 90°. So the above angle is measured as 90°.

Question 2.
If you didn’t have a protractor, how could you construct one? Use words, pictures, or numbers to explain in the space below.