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- anonymous

What are the measures of Angles a, b, and c? Show your work and explain your answers.
I found out a and c but i need to find out b, please help

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- schrodinger

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- anonymous

- anonymous

A = 40
B = ?
C = 105

- nerdyotter

We'll start with basic knowledge of triangles. Every triangle in Euclidean geometry adds to 180 degrees in total.
Angle (a) is equal to 30 degrees, since it is vertical angles with a 30-degree angle. The triangle which contains angle (a) is a right triangle, meaning one of the degree measures is 90 degrees. If you add 90 degrees and 30 degrees, you get 120 degrees.
Subtract 120 degrees from the total measure of every triangle in Euclidean geometry (180 degrees) to get the measure of your missing angle (angle b).

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- anonymous

i mean 180 - 120

- nerdyotter

Correct!

- anonymous

\(\bf\color{blue}{Thank~You!!}\)

- nerdyotter

@TerriKirkland Of course! Taking a similar course myself at the moment and it's always nice to help out a fellow student. :)

- anonymous

but wait @nerdyotter does that say angle a is 30?

- nerdyotter

@TerriKirkland Yep! The measure of any two vertical angles are always going to be congruent. Angle (a) is vertical angles with a thirty degree angle. Therefore, angle (a) is a 30-degree angle itself.

- anonymous

I thought it couldn't be 30 degrees since the angle above it is 30 degrees

- nerdyotter

Vertical angles are always congruent in Euclidean geometry. Take the attached diagram, for example. The measure of angle 1 and angle 3 are going to be congruent (the same), and the measure of angle 2 and angle 4 are going to be congruent (the same).
Here's a link to a site explaining it if you need further examples: http://www.mathwarehouse.com/geometry/angle/vertical-angles.php

- anonymous

oooh that make since thank you so much!♥

- anonymous

Thanks for the website also haha

- nerdyotter

@TerriKirkland No problem! Feel free to tag me or message me if you need any further help.

- anonymous

You got it☺

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