Math / Geometry

Question23. Model With Mathematics A glazier is setting upports in parallel segments to prevent glass breakage during storms. What are the values of $x$ and $y$ ? Justify your conclusions.
24. Reason In the parking lot shown, all of the lines for the parking spaces should be parallel. If $m \angle 3=61^{\circ}$ , what should $m \angle 1$ and $m \angle 2$ be? Explain.

Studdy Solution

STEP 1

1. For Problem 23, the window forms a parallelogram, which means opposite angles are equal, and adjacent angles are supplementary.
2. For Problem 24, the parking lines should be parallel, and the angles are formed by a transversal intersecting parallel lines. Corresponding angles and alternate interior angles are equal.

STEP 2

1. Solve Problem 23: Determine the values of $x$ and $y$ .
2. Solve Problem 24: Determine the measures of $\angle 1$ and $\angle 2$ .

STEP 3

Identify the properties of a parallelogram. In a parallelogram, opposite angles are equal, and adjacent angles are supplementary (sum to $180^\circ$ ).

STEP 4

Given one angle is $50^\circ$ , the opposite angle is also $50^\circ$ . Therefore, if $x$ is opposite to the $50^\circ$ angle, then $x = 50^\circ$ .

STEP 5

Adjacent angles in a parallelogram are supplementary. Therefore, if $y$ is adjacent to the $50^\circ$ angle, then:
$y + 50^\circ = 180^\circ$ $y = 180^\circ - 50^\circ$ $y = 130^\circ$

STEP 6

For Problem 24, identify the properties of parallel lines cut by a transversal. Corresponding angles are equal, and alternate interior angles are equal.

STEP 7

Given $m \angle 3 = 61^\circ$ , and assuming $\angle 3$ is a corresponding angle to $\angle 1$ , then:
$m \angle 1 = 61^\circ$

STEP 8

Assuming $\angle 2$ is an alternate interior angle to $\angle 3$ , then:
$m \angle 2 = 61^\circ$
The values are: - For Problem 23: $x = 50^\circ$ , $y = 130^\circ$ - For Problem 24: $m \angle 1 = 61^\circ$ , $m \angle 2 = 61^\circ$

Was this helpful?

Studdy Solution

STEP 1

STEP 2

1. Solve Problem 23: Determine the values of $x$ and $y$ .
2. Solve Problem 24: Determine the measures of $\angle 1$ and $\angle 2$ .

STEP 3

Identify the properties of a parallelogram. In a parallelogram, opposite angles are equal, and adjacent angles are supplementary (sum to $180^\circ$ ).

STEP 4

Given one angle is $50^\circ$ , the opposite angle is also $50^\circ$ . Therefore, if $x$ is opposite to the $50^\circ$ angle, then $x = 50^\circ$ .

STEP 5

Adjacent angles in a parallelogram are supplementary. Therefore, if $y$ is adjacent to the $50^\circ$ angle, then:
$y + 50^\circ = 180^\circ$ $y = 180^\circ - 50^\circ$ $y = 130^\circ$

STEP 6

For Problem 24, identify the properties of parallel lines cut by a transversal. Corresponding angles are equal, and alternate interior angles are equal.

STEP 7

Given $m \angle 3 = 61^\circ$ , and assuming $\angle 3$ is a corresponding angle to $\angle 1$ , then:
$m \angle 1 = 61^\circ$

STEP 8

Assuming $\angle 2$ is an alternate interior angle to $\angle 3$ , then:
$m \angle 2 = 61^\circ$
The values are: - For Problem 23: $x = 50^\circ$ , $y = 130^\circ$ - For Problem 24: $m \angle 1 = 61^\circ$ , $m \angle 2 = 61^\circ$

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Studdy Solution

STEP 1

STEP 2

1. Solve Problem 23: Determine the values of xxx and yyy.2. Solve Problem 24: Determine the measures of ∠1\angle 1∠1 and ∠2\angle 2∠2.

STEP 3

Identify the properties of a parallelogram. In a parallelogram, opposite angles are equal, and adjacent angles are supplementary (sum to 180∘180^\circ180∘).

STEP 4

Given one angle is 50∘50^\circ50∘, the opposite angle is also 50∘50^\circ50∘. Therefore, if xxx is opposite to the 50∘50^\circ50∘ angle, then x=50∘x = 50^\circx=50∘.

STEP 5

Adjacent angles in a parallelogram are supplementary. Therefore, if yyy is adjacent to the 50∘50^\circ50∘ angle, then:y+50∘=180∘ y + 50^\circ = 180^\circ y+50∘=180∘ y=180∘−50∘ y = 180^\circ - 50^\circ y=180∘−50∘ y=130∘ y = 130^\circ y=130∘

STEP 6

For Problem 24, identify the properties of parallel lines cut by a transversal. Corresponding angles are equal, and alternate interior angles are equal.

STEP 7

Given m∠3=61∘m \angle 3 = 61^\circm∠3=61∘, and assuming ∠3\angle 3∠3 is a corresponding angle to ∠1\angle 1∠1, then:m∠1=61∘ m \angle 1 = 61^\circ m∠1=61∘

STEP 8

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

1. Solve Problem 23: Determine the values of $x$ and $y$ .
2. Solve Problem 24: Determine the measures of $\angle 1$ and $\angle 2$ .

Identify the properties of a parallelogram. In a parallelogram, opposite angles are equal, and adjacent angles are supplementary (sum to $180^\circ$ ).

Given one angle is $50^\circ$ , the opposite angle is also $50^\circ$ . Therefore, if $x$ is opposite to the $50^\circ$ angle, then $x = 50^\circ$ .

Adjacent angles in a parallelogram are supplementary. Therefore, if $y$ is adjacent to the $50^\circ$ angle, then:
$y + 50^\circ = 180^\circ$ $y = 180^\circ - 50^\circ$ $y = 130^\circ$

Given $m \angle 3 = 61^\circ$ , and assuming $\angle 3$ is a corresponding angle to $\angle 1$ , then:
$m \angle 1 = 61^\circ$