Math / Geometry

Question```latex Identify all the numbered angles that are congruent to the given angle.
List the numbers of any angles that are congruent to the given angle. $\square$ (Use a comma to separate answers as needed. Do not include the $\angle$ symbol in your answer.) ```

Studdy Solution

STEP 1

What is this asking? Which angles have the same measurement as angle 2, which is $50^\circ$ ? Watch out! Don't mix up corresponding and vertical angles!

STEP 2

1. Find the vertical angle
2. Find the corresponding angle
3. Find the other vertical angle

STEP 3

We're given that angle 2 is $50^\circ$ .
We're looking for congruent angles, which means angles with the same measurement.
Let's start by looking for a vertical angle.
Vertical angles are formed by intersecting lines and are opposite each other.

STEP 4

Angle 4 is the vertical angle to angle 2.
Vertical angles are always congruent.
So, angle 4 is also $50^\circ$ !

STEP 5

Now, let's think about corresponding angles.
These are angles that are in the same position when a line crosses two parallel lines.
Since the lines are parallel, corresponding angles are congruent.

STEP 6

Angle 2 and angle 6 are corresponding angles.
Since angle 2 is $50^\circ$ , angle 6 must also be $50^\circ$ !

STEP 7

We found that angle 6 is $50^\circ$ .
Let's find its vertical angle.

STEP 8

Angle 8 is vertical to angle 6.
Since vertical angles are congruent, angle 8 must also be $50^\circ$ !

STEP 9

Angles 4, 6, and 8 are congruent to angle 2.
So our answer is 4, 6, 8.

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Question```latex Identify all the numbered angles that are congruent to the given angle.
List the numbers of any angles that are congruent to the given angle. $\square$ (Use a comma to separate answers as needed. Do not include the $\angle$ symbol in your answer.) ```

Studdy Solution

STEP 1

What is this asking? Which angles have the same measurement as angle 2, which is $50^\circ$ ? Watch out! Don't mix up corresponding and vertical angles!

STEP 2

1. Find the vertical angle
2. Find the corresponding angle
3. Find the other vertical angle

STEP 3

We're given that angle 2 is $50^\circ$ .
We're looking for congruent angles, which means angles with the same measurement.
Let's start by looking for a vertical angle.
Vertical angles are formed by intersecting lines and are opposite each other.

STEP 4

Angle 4 is the vertical angle to angle 2.
Vertical angles are always congruent.
So, angle 4 is also $50^\circ$ !

STEP 5

Now, let's think about corresponding angles.
These are angles that are in the same position when a line crosses two parallel lines.
Since the lines are parallel, corresponding angles are congruent.

STEP 6

Angle 2 and angle 6 are corresponding angles.
Since angle 2 is $50^\circ$ , angle 6 must also be $50^\circ$ !

STEP 7

We found that angle 6 is $50^\circ$ .
Let's find its vertical angle.

STEP 8

Angle 8 is vertical to angle 6.
Since vertical angles are congruent, angle 8 must also be $50^\circ$ !

STEP 9

Angles 4, 6, and 8 are congruent to angle 2.
So our answer is 4, 6, 8.

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Question```latex Identify all the numbered angles that are congruent to the given angle.List the numbers of any angles that are congruent to the given angle. □\square□ (Use a comma to separate answers as needed. Do not include the ∠\angle∠ symbol in your answer.) ```

Studdy Solution

STEP 1

What is this asking? Which angles have the same measurement as angle 2, which is 50∘50^\circ50∘? Watch out! Don't mix up corresponding and vertical angles!

STEP 2

1. Find the vertical angle2. Find the corresponding angle3. Find the other vertical angle

STEP 3

We're given that angle 2 is 50∘50^\circ50∘.We're looking for **congruent angles**, which means angles with the *same measurement*.Let's start by looking for a **vertical angle**.Vertical angles are formed by intersecting lines and are *opposite* each other.

STEP 4

Angle 4 is the vertical angle to angle 2.Vertical angles are **always congruent**.So, angle 4 is also 50∘50^\circ50∘!

STEP 5

Now, let's think about **corresponding angles**.These are angles that are in the *same position* when a line crosses two parallel lines.Since the lines are parallel, corresponding angles are **congruent**.

STEP 6

Angle 2 and angle 6 are corresponding angles.Since angle 2 is 50∘50^\circ50∘, angle 6 must also be 50∘50^\circ50∘!

STEP 7

We found that angle 6 is 50∘50^\circ50∘.Let's find its vertical angle.

STEP 8

Angle 8 is vertical to angle 6.Since vertical angles are congruent, angle 8 must also be 50∘50^\circ50∘!

STEP 9

Angles 4, 6, and 8 are congruent to angle 2.So our answer is 4, 6, 8.

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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.

Question```latex Identify all the numbered angles that are congruent to the given angle.
List the numbers of any angles that are congruent to the given angle. $\square$ (Use a comma to separate answers as needed. Do not include the $\angle$ symbol in your answer.) ```

What is this asking? Which angles have the same measurement as angle 2, which is $50^\circ$ ? Watch out! Don't mix up corresponding and vertical angles!

1. Find the vertical angle
2. Find the corresponding angle
3. Find the other vertical angle

We're given that angle 2 is $50^\circ$ .
We're looking for congruent angles, which means angles with the same measurement.
Let's start by looking for a vertical angle.
Vertical angles are formed by intersecting lines and are opposite each other.

Angle 4 is the vertical angle to angle 2.
Vertical angles are always congruent.
So, angle 4 is also $50^\circ$ !

Now, let's think about corresponding angles.
These are angles that are in the same position when a line crosses two parallel lines.
Since the lines are parallel, corresponding angles are congruent.

Angle 2 and angle 6 are corresponding angles.
Since angle 2 is $50^\circ$ , angle 6 must also be $50^\circ$ !

We found that angle 6 is $50^\circ$ .
Let's find its vertical angle.

Angle 8 is vertical to angle 6.
Since vertical angles are congruent, angle 8 must also be $50^\circ$ !

Angles 4, 6, and 8 are congruent to angle 2.
So our answer is 4, 6, 8.