# Eureka Math Geometry Module 1 Lesson 7 Answer Key

## Engage NY Eureka Math Geometry Module 1 Lesson 7 Answer Key

### Eureka Math Geometry Module 1 Lesson 7 Example Answer Key

Examples

Example 1.

m∠a =
m∠a=48°

Example 2.

m∠b=
m∠b=132°

Example 3.

m∠c=
m∠c=48°

Example 4.

m∠d=
m∠d=48°

Example 5.
An ___ is sometimes useful when solving for unknown angles. In this figure, we can use the auxiliary line to find the measures of ∠e and ∠f (how?) and then add the two measures together to find the measure of ∠W.
What is the measure of ∠W?

An auxiliary line is sometimes useful when solving for unknown angles.
In this figure, we can use the auxiliary line to find the measures of ∠e and ∠f (how?) and then add the two measures together to find the measure of ∠W.
What is the measure of ∠W?
m∠e=41°, m∠f=35°, m∠W=76°

### Eureka Math Geometry Module 1 Lesson 7 Exercise Answer Key

Opening Exercise
Use the diagram at the right to determine x and y. $$\overleftrightarrow{A B}$$ and $$\overleftrightarrow{C D}$$ are straight lines.

x =
y=
x=30
y=52

Name a pair of vertical angles:
∠AOC, ∠DOB

Find the measure of ∠BOF. Justify your calculation.
m∠BOF=32° Linear pairs form supplementary angles.

Discussion
Given line AB and line CD in a plane (see the diagram below), a third line EF is called a transversal if it intersects (AB) ⃡ at a single point and intersects (CD) ⃡ at a single but different point. Line AB and line CD are parallel if and only if the following types of angle pairs are congruent or supplementary:

→ Corresponding angles are equal in measure.
∠a and ∠e , ∠d and ∠h, etc.

→ Alternate interior angles are equal in measure.
∠c and ∠f, ∠d and ∠e

→ Same-side interior angles are supplementary.
∠c and ∠e, ∠d and ∠f

Exercises 1–10
In each exercise below, find the unknown (labeled) angles. Give reasons for your solutions.

Exercise 1.

m∠a=
m∠a=53°
If parallel lines are cut by a transversal, then corresponding angles are equal in measure.

m∠b=
m∠b=53°
Vertical angles are equal in measure.

m∠c=
m∠c=127°
If parallel lines are cut by a transversal, then interior angles on the same side are supplementary.

Exercise 2.

m∠d=
m∠d=145°
Linear pairs form supplementary angles;
if parallel lines are cut by a transversal, then alternate interior angles are equal in measure.

Exercise 3.

m∠e=
m∠e=54°
If parallel lines are cut by a transversal, then alternate interior angles are equal in measure.

m∠f=
m∠f=68°
Vertical angles are equal in measure;
if parallel lines are cut by a transversal, then interior angles on the same side are supplementary.

Exercise 4.

m∠g=
m∠g=92°
Vertical angles are equal in measure;
if parallel lines are cut by a transversal, then interior angles on the same side are supplementary.

Exercise 5.

m∠h=
m∠h=100°
If parallel lines are cut by a transversal, then interior angles on the same side are supplementary.

Exercise 6.

m∠i=
m∠i=114°
Linear pairs form supplementary angles;
if parallel lines are cut by a transversal, then alternate interior angles are equal in measure.

Exercise 7.

m∠j=
m∠j=92°
If parallel lines are cut by a transversal, then alternate interior angles are equal in measure.

m∠k=
m∠k=42°
Consecutive adjacent angles on a line sum to 180°.

m∠m=
m∠m=46°
If parallel lines are cut by a transversal, then alternate interior angles are equal in measure.

Exercise 8.

m∠n=
m∠n=81°
If parallel lines are cut by a transversal, then corresponding angles are equal in measure.

Exercise 9.

m∠p=
m∠p=18°
Consecutive adjacent angles on a line sum to 180°.

m∠q=
m∠q=94°
If parallel lines are cut by a transversal, then corresponding angles are equal in measure.

Exercise 10.

m∠r=
m∠r=46°
If parallel lines are cut by a transversal, then interior angles on the same side are supplementary; if parallel lines are cut by a transversal, then alternate interior angles are equal in measure.

### Eureka Math Geometry Module 1 Lesson 7 Problem Set Answer Key

Find the unknown (labeled) angles. Give reasons for your solutions.

Question 1.

m∠a=
m∠a=40°
If parallel lines are cut by a transversal, then alternate interior angles are equal in measure.

Question 2.

m∠b=
m∠b=48°
If parallel lines are cut by a transversal, then corresponding angles are equal in measure.

m∠c=
m∠c=46°
Vertical angles are equal in measure;
if parallel lines are cut by a transversal, then alternate interior angles are equal in measure.

Exercise 3.

m∠d=
m∠d=50°
If parallel lines are cut by a transversal, then alternate interior angles are equal in measure.

m∠e=
m∠e=50°
If parallel lines are cut by a transversal, then alternate interior angles are equal in measure.

Exercise 4.

m∠f=
m∠f=82°
If parallel lines are cut by a transversal, then interior angles on the same side are supplementary; vertical angles are equal in measure.

### Eureka Math Geometry Module 1 Lesson 7 Exit Ticket Answer Key

Determine the value of each variable.

x =
y =
z =