Math / Geometry

Question```latex Find the measure of the numbered angle.
$m \angle 4=$
Angle 8 should equal 140.
Angles 1 and 3, and angles 2 and 4 are vertical.

Studdy Solution

STEP 1

What is this asking? We need to find the measure of angle 4, given that angle 1 is 40 degrees and some other angles are 90 degrees. Watch out! Don't get tricked by the extra information!
We need to focus on the relationship between the given angle and the one we're looking for.

STEP 2

1. Find the relationship between angle 1 and angle 4.
2. Calculate the measure of angle 4.

STEP 3

Alright, so we're given that angles 1 and 3 are vertical angles.
Remember, vertical angles are always equal!
So, if $m\angle 1 = 40^\circ$ , then $m\angle 3 = 40^\circ$ as well!

STEP 4

We're also told that angles 2 and 4 are vertical angles.
That means they're equal too!
This is great news!

STEP 5

Notice that angles 1, 2, and 3 form a straight line.
A straight line always measures $180^\circ$ .
This means the sum of angles 1, 2, and 3 is $180^\circ$ .
We can write this as: $m\angle 1 + m\angle 2 + m\angle 3 = 180^\circ$ .

STEP 6

We know $m\angle 1 = 40^\circ$ and $m\angle 3 = 40^\circ$ , so we can substitute those values: $40^\circ + m\angle 2 + 40^\circ = 180^\circ$ .

STEP 7

Combining the known values, we get $80^\circ + m\angle 2 = 180^\circ$ .

STEP 8

To find the measure of angle 2, we can subtract $80^\circ$ from both sides of the equation: $m\angle 2 = 180^\circ - 80^\circ$ .

STEP 9

This gives us $m\angle 2 = 100^\circ$ .
Awesome!

STEP 10

Since angles 2 and 4 are vertical angles, they are equal.
Therefore, $m\angle 4 = m\angle 2 = 100^\circ$ .
Boom!

STEP 11

The measure of angle 4 is $100^\circ$ .

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Question```latex Find the measure of the numbered angle.
$m \angle 4=$
Angle 8 should equal 140.
Angles 1 and 3, and angles 2 and 4 are vertical.

Studdy Solution

STEP 1

What is this asking? We need to find the measure of angle 4, given that angle 1 is 40 degrees and some other angles are 90 degrees. Watch out! Don't get tricked by the extra information!
We need to focus on the relationship between the given angle and the one we're looking for.

STEP 2

1. Find the relationship between angle 1 and angle 4.
2. Calculate the measure of angle 4.

STEP 3

Alright, so we're given that angles 1 and 3 are vertical angles.
Remember, vertical angles are always equal!
So, if $m\angle 1 = 40^\circ$ , then $m\angle 3 = 40^\circ$ as well!

STEP 4

We're also told that angles 2 and 4 are vertical angles.
That means they're equal too!
This is great news!

STEP 5

Notice that angles 1, 2, and 3 form a straight line.
A straight line always measures $180^\circ$ .
This means the sum of angles 1, 2, and 3 is $180^\circ$ .
We can write this as: $m\angle 1 + m\angle 2 + m\angle 3 = 180^\circ$ .

STEP 6

We know $m\angle 1 = 40^\circ$ and $m\angle 3 = 40^\circ$ , so we can substitute those values: $40^\circ + m\angle 2 + 40^\circ = 180^\circ$ .

STEP 7

Combining the known values, we get $80^\circ + m\angle 2 = 180^\circ$ .

STEP 8

To find the measure of angle 2, we can subtract $80^\circ$ from both sides of the equation: $m\angle 2 = 180^\circ - 80^\circ$ .

STEP 9

This gives us $m\angle 2 = 100^\circ$ .
Awesome!

STEP 10

Since angles 2 and 4 are vertical angles, they are equal.
Therefore, $m\angle 4 = m\angle 2 = 100^\circ$ .
Boom!

STEP 11

The measure of angle 4 is $100^\circ$ .

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Question```latex Find the measure of the numbered angle.m∠4=m \angle 4=m∠4=Angle 8 should equal 140.Angles 1 and 3, and angles 2 and 4 are vertical.

Studdy Solution

STEP 1

What is this asking? We need to find the measure of angle 4, given that angle 1 is 40 degrees and some other angles are 90 degrees. Watch out! Don't get tricked by the extra information!We need to focus on the relationship between the given angle and the one we're looking for.

STEP 2

1. Find the relationship between angle 1 and angle 4.2. Calculate the measure of angle 4.

STEP 3

Alright, so we're given that angles 1 and 3 are **vertical angles**.Remember, vertical angles are **always equal**!So, if m∠1=40∘m\angle 1 = 40^\circm∠1=40∘, then m∠3=40∘m\angle 3 = 40^\circm∠3=40∘ as well!

STEP 4

We're also told that angles 2 and 4 are **vertical angles**.That means they're equal too!This is great news!

STEP 5

Notice that angles 1, 2, and 3 form a **straight line**.A straight line always measures 180∘180^\circ180∘.This means the sum of angles 1, 2, and 3 is 180∘180^\circ180∘.We can write this as: m∠1+m∠2+m∠3=180∘m\angle 1 + m\angle 2 + m\angle 3 = 180^\circm∠1+m∠2+m∠3=180∘.

STEP 6

We know m∠1=40∘m\angle 1 = 40^\circm∠1=40∘ and m∠3=40∘m\angle 3 = 40^\circm∠3=40∘, so we can substitute those values: 40∘+m∠2+40∘=180∘40^\circ + m\angle 2 + 40^\circ = 180^\circ40∘+m∠2+40∘=180∘.

STEP 7

Combining the known values, we get 80∘+m∠2=180∘80^\circ + m\angle 2 = 180^\circ80∘+m∠2=180∘.

STEP 8

To find the measure of angle 2, we can subtract 80∘80^\circ80∘ from both sides of the equation: m∠2=180∘−80∘m\angle 2 = 180^\circ - 80^\circm∠2=180∘−80∘.

STEP 9

This gives us m∠2=100∘m\angle 2 = 100^\circm∠2=100∘.Awesome!

STEP 10

Since angles 2 and 4 are vertical angles, they are equal.Therefore, m∠4=m∠2=100∘m\angle 4 = m\angle 2 = 100^\circm∠4=m∠2=100∘.Boom!

STEP 11

The measure of angle 4 is 100∘100^\circ100∘.

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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 Find the measure of the numbered angle.
$m \angle 4=$
Angle 8 should equal 140.
Angles 1 and 3, and angles 2 and 4 are vertical.

What is this asking? We need to find the measure of angle 4, given that angle 1 is 40 degrees and some other angles are 90 degrees. Watch out! Don't get tricked by the extra information!
We need to focus on the relationship between the given angle and the one we're looking for.

1. Find the relationship between angle 1 and angle 4.
2. Calculate the measure of angle 4.

Alright, so we're given that angles 1 and 3 are vertical angles.
Remember, vertical angles are always equal!
So, if $m\angle 1 = 40^\circ$ , then $m\angle 3 = 40^\circ$ as well!

We're also told that angles 2 and 4 are vertical angles.
That means they're equal too!
This is great news!

Notice that angles 1, 2, and 3 form a straight line.
A straight line always measures $180^\circ$ .
This means the sum of angles 1, 2, and 3 is $180^\circ$ .
We can write this as: $m\angle 1 + m\angle 2 + m\angle 3 = 180^\circ$ .

We know $m\angle 1 = 40^\circ$ and $m\angle 3 = 40^\circ$ , so we can substitute those values: $40^\circ + m\angle 2 + 40^\circ = 180^\circ$ .

Combining the known values, we get $80^\circ + m\angle 2 = 180^\circ$ .

To find the measure of angle 2, we can subtract $80^\circ$ from both sides of the equation: $m\angle 2 = 180^\circ - 80^\circ$ .

This gives us $m\angle 2 = 100^\circ$ .
Awesome!

Since angles 2 and 4 are vertical angles, they are equal.
Therefore, $m\angle 4 = m\angle 2 = 100^\circ$ .
Boom!

The measure of angle 4 is $100^\circ$ .