## 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 =

Answer:

m∠a=48°

Example 2.

m∠b=

Answer:

m∠b=132°

Example 3.

m∠c=

Answer:

m∠c=48°

Example 4.

m∠d=

Answer:

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?

Answer:

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?

Answer:

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=

Answer:

x=30

y=52

Name a pair of vertical angles:

Answer:

∠AOC, ∠DOB

Find the measure of ∠BOF. Justify your calculation.

Answer:

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.

Answer:

∠a and ∠e , ∠d and ∠h, etc.

→ Alternate interior angles are equal in measure.

Answer:

∠c and ∠f, ∠d and ∠e

→ Same-side interior angles are supplementary.

Answer:

∠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=

Answer:

m∠a=53°

If parallel lines are cut by a transversal, then corresponding angles are equal in measure.

m∠b=

Answer:

m∠b=53°

Vertical angles are equal in measure.

m∠c=

Answer:

m∠c=127°

If parallel lines are cut by a transversal, then interior angles on the same side are supplementary.

Exercise 2.

m∠d=

Answer:

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=

Answer:

m∠e=54°

If parallel lines are cut by a transversal, then alternate interior angles are equal in measure.

m∠f=

Answer:

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=

Answer:

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=

Answer:

m∠h=100°

If parallel lines are cut by a transversal, then interior angles on the same side are supplementary.

Exercise 6.

m∠i=

Answer:

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=

Answer:

m∠j=92°

If parallel lines are cut by a transversal, then alternate interior angles are equal in measure.

m∠k=

Answer:

m∠k=42°

Consecutive adjacent angles on a line sum to 180°.

m∠m=

Answer:

m∠m=46°

If parallel lines are cut by a transversal, then alternate interior angles are equal in measure.

Exercise 8.

m∠n=

Answer:

m∠n=81°

If parallel lines are cut by a transversal, then corresponding angles are equal in measure.

Exercise 9.

m∠p=

Answer:

m∠p=18°

Consecutive adjacent angles on a line sum to 180°.

m∠q=

Answer:

m∠q=94°

If parallel lines are cut by a transversal, then corresponding angles are equal in measure.

Exercise 10.

m∠r=

Answer:

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=

Answer:

m∠a=40°

If parallel lines are cut by a transversal, then alternate interior angles are equal in measure.

Question 2.

m∠b=

Answer:

m∠b=48°

If parallel lines are cut by a transversal, then corresponding angles are equal in measure.

m∠c=

Answer:

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=

Answer:

m∠d=50°

If parallel lines are cut by a transversal, then alternate interior angles are equal in measure.

m∠e=

Answer:

m∠e=50°

If parallel lines are cut by a transversal, then alternate interior angles are equal in measure.

Exercise 4.

m∠f=

Answer:

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 =

Answer:

x= 28.75

y=135.5

z=44.5