## Engage NY Eureka Math Geometry Module 1 Lesson 6 Answer Key

### Eureka Math Geometry Module 1 Lesson 6 Example Answer Key

Example

Find the measure of each labeled angle. Give a reason for your solution.

Answer:

### Eureka Math Geometry Module 1 Lesson 6 Exercise Answer Key

Opening Exercise

Determine the measure of the missing angle in each diagram.

Answer:

What facts about angles did you use?

Answer:

Answers may include the following: vertical angles are equal in measure; linear pairs form supplementary angles; angles at a point sum to 360°.

Discussion

Two angles ∠AOC and ∠COB, with a common side \(\overrightarrow{O C}\), are __ if C belongs to the interior of ∠AOB.

The sum of angles on a straight line is 180°, and two such angles are called a linear pair. Two angles are called supplementary if the sum of their measures is __; two angles are called complementary if the sum of their measures is ___. Describing angles as supplementary or complementary refers only to the measures of their angles. The positions of the angles or whether the pair of angles is adjacent to each other is not part of the definition.

Answer:

Two angles ∠AOC and ∠COB, with a common side \(\overrightarrow{O C}\), are __adjacent angles__ if C belongs to the interior of ∠AOB. The sum of angles on a straight line is 180°, and two such angles are called a linear pair. Two angles are called supplementary if the sum of their measures is __180°__; two angles are called complementary if the sum of their measures is __90°__. Describing angles as supplementary or complementary refers only to the measures of their angles. The positions of the angles or whether the pair of angles is adjacent to each other is not part of the definition.

In the figure, line segment AD is drawn.

Find m∠DCE.

Answer:

m∠DCE=18°

The total measure of adjacent angles around a point is __.

Answer:

The total measure of adjacent angles around a point is __360°__.

Find the measure of ∠HKI.

Answer:

m∠HKI=80°

Vertical angles have __ measure. Two angles are vertical if their sides form opposite rays.

Answer:

Vertical angles have __equal__ measure. Two angles are vertical if their sides form opposite rays.

Find m∠TRV.

Answer:

m∠TRV=52°

Exercises

In the figures below, \(\overline{A B}\), \(\overline{C D}\), and \(\overline{E F}\) are straight line segments. Find the measure of each marked angle, or find the unknown numbers labeled by the variables in the diagrams. Give reasons for your calculations. Show all the steps to your solutions.

Exercise 1.

Answer:

m∠a=36°

Linear pairs form supplementary angles.

Exercise 2.

Answer:

m∠b=47°

Consecutive adjacent angles on a line sum to 180°.

Exercise 3.

Answer:

m∠c=14°

Consecutive adjacent angles on a line sum to 180°

Exercise 4.

Answer:

m∠d=49°

Consecutive adjacent angles on a line sum to 180°

Exercise 5.

Answer:

m∠g=29°

Angles at a point sum to 360°.

For Exercises 6–12, find the values of x and y. Show all work.

Exercise 6.

Answer:

x=80

Angles at a point sum to 360°.

Exercise 7.

Answer:

x=30; y=90

Vertical angles are equal in measure.

Angles at a point sum to 360°.

Exercise 8.

Answer:

x=20

Vertical angles are equal in measure.

Consecutive adjacent angles on a line sum to 180°.

Exercise 9.

Answer:

x=39; y=123

Vertical angles are equal in measure. Angles at a point sum to 360°.

Exercise 10.

Answer:

x=80; y=122

Consecutive adjacent angles on a line sum to 180°.

Exercise 11.

Answer:

x=10; y=112

Consecutive adjacent angles on a line sum to 180°. Vertical angles are equal in measure.

Exercise 12.

Answer:

x=27; y=47

Consecutive adjacent angles on a line sum to 180°. Vertical angles are equal in measure.

### Eureka Math Geometry Module 1 Lesson 6 Problem Set Answer Key

In the figures below, \(\overline{A B}\) and \(\overline{C D}\) are straight line segments. Find the value of x and/or y in each diagram below.

Show all the steps to your solutions, and give reasons for your calculations.

Question 1.

Answer:

x=133

y=43

Angle addition postulate Linear pairs form supplementary angles.

Question 2.

Answer:

x=78

Consecutive adjacent angles on a line sum to 180°.

Question 3.

Answer:

x=20

y=110

Consecutive adjacent angles on a line sum to 180°. Vertical angles are equal in measure.

### Eureka Math Geometry Module 1 Lesson 6 Exit Ticket Answer Key

Use the following diagram to answer the questions below:

Question 1.

Name an angle supplementary to ∠HZJ, and provide the reason for your calculation.

Answer:

∠JZF or ∠HZG

Linear pairs form supplementary angles.

b. Name an angle complementary to ∠HZJ, and provide the reason for your calculation.

Answer:

∠JZA

The angles sum to 90°.

Question 2.

If m∠HZJ=38°, what is the measure of each of the following angles? Provide reasons for your calculations.

a. m∠FZG

Answer:

38°

b. m∠HZG

Answer:

142°

c. m∠AZJ

Answer:

52°