Math  /  Geometry

Question5. Given m6=142m \angle 6=142^{\circ}, find the measure of each missing ang a. m1=m \angle 1= b. m2=m \angle 2= c. m3=m \angle 3= d. m4=m \angle 4= e. m<5=m<5=
5. 8007=8007=

Studdy Solution

STEP 1

What is this asking? If we know one angle made by a line crossing two parallel lines, can we figure out all the other angles? Watch out! Don't mix up which angles are equal and which angles add up to 180180^\circ!

STEP 2

1. Angle 2
2. Angle 1
3. Angle 4
4. Angle 3 and 5
5. Angle 7

STEP 3

We're given that m6=142m\angle 6 = 142^\circ.
Angles 2 and 6 are **vertical angles**, which means they're **opposite** each other formed by intersecting lines.
Vertical angles are **always equal**!

STEP 4

So, m2=m6=142m\angle 2 = m\angle 6 = \mathbf{142^\circ}!

STEP 5

Angles 1 and 2 are **supplementary angles**.
This means they're next to each other and add up to 180180^\circ.
Think of it like this: a straight line is 180180^\circ, and angles 1 and 2 together make a straight line!

STEP 6

We know m2=142m\angle 2 = 142^\circ.
So, m1+m2=180m\angle 1 + m\angle 2 = 180^\circ.
Let's plug in what we know: m1+142=180m\angle 1 + 142^\circ = 180^\circ.

STEP 7

To find m1m\angle 1, we **subtract** 142142^\circ from both sides: m1=180142=38m\angle 1 = 180^\circ - 142^\circ = \mathbf{38^\circ}!

STEP 8

Just like angles 2 and 6, angles 1 and 4 are **vertical angles**.
So, they're equal!

STEP 9

Since m1=38m\angle 1 = 38^\circ, we know m4=38m\angle 4 = \mathbf{38^\circ} as well!

STEP 10

Now, let's look at the other parallel line.
Angles 3 and 6 are **corresponding angles**.
Corresponding angles are in matching positions when a line crosses two parallel lines, and they're **always equal**!

STEP 11

Since m6=142m\angle 6 = 142^\circ, we know m3=142m\angle 3 = \mathbf{142^\circ}!

STEP 12

Angles 5 and 1 are also corresponding angles.
Since m1=38m\angle 1 = 38^\circ, then m5=38m\angle 5 = \mathbf{38^\circ}!

STEP 13

Angles 7 and 3 are vertical angles, so they must be equal.
Since m3=142m\angle 3 = 142^\circ, then m7=142m\angle 7 = \mathbf{142^\circ}!
We could have also used the fact that angles 7 and 5 are supplementary, or that angles 7 and 6 are corresponding.
So many ways to find the answer!

STEP 14

m1=38m\angle 1 = 38^\circ m2=142m\angle 2 = 142^\circ m3=142m\angle 3 = 142^\circm4=38m\angle 4 = 38^\circm5=38m\angle 5 = 38^\circm7=142m\angle 7 = 142^\circ

Was this helpful?

Studdy solves anything!

banner

Start learning now

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

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord