GED Triangle Geometry Question

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I am studying Geometry in a GED book. One of the questions in the practice section wasn't covered in the text. Can you help me understand what the question is saying and how to work it? I will post a link to a picture of it I took because it involves a diagram.

Thank you.

https://postimg.org/image/7ej122sxz/
 
I am studying Geometry in a GED book. One of the questions in the practice section wasn't covered in the text. Can you help me understand what the question is saying and how to work it? I will post a link to a picture of it I took because it involves a diagram.

geometry_question.jpg
You are given four angle measures and some relationships. You are being asked to figure out the length of the horizontal line. You have been given a hint as to how to proceed.

What is the measure of angle BAC? (Hint: Subtract.)

What is the measure of angle BCA? (Hint: Subtract.)

What methods have you learned in class? For instance, have you studied the Law of Sines?

Thank you! ;)
 
I am studying Geometry in a GED book. One of the questions in the practice section wasn't covered in the text. Can you help me understand what the question is saying and how to work it? I will post a link to a picture of it I took because it involves a diagram.
From the given, it is easy to show that ΔABC\displaystyle \Delta ABC is an equilateral triangle.
Hint: all its angle have the same measure.
 
Misunderstanding the terms

You are given four angle measures and some relationships. You are being asked to figure out the length of the horizontal line. You have been given a hint as to how to proceed.

What is the measure of angle BAC? (Hint: Subtract.)

What is the measure of angle BCA? (Hint: Subtract.)

What methods have you learned in class? For instance, have you studied the Law of Sines?

Thank you! ;)

Ok, I am having a problem just understanding the problem as it is written. They did not explain the terms that they have used in this problem in the text. All that they explained was a single triangle, would be named DEF, and that <D is an angle in a single triangle that you can say what it measures, and that all angles measure to 180 degrees in a triangle. Here they have a picture of two triangles together, and the measurements that they speak of <DAB and <DCB are not in a single triangle, but are connected lines through two triangles. So, I am unsure how to understand what they mean by <DAB measures 115. What exactly is that measurement for? Like, in the picture I can see that you could say <A ... that specific angle measures 55 degrees. When you have < with three letters, what does it mean? I haven't learned anything else like the Law of Sines that you mentioned, just that you can classify triangles by side lengths (equilateral, isosceles, scalene) and angle measures (right, acute, and obtuse). I hope that made sense. Thank you. :)
 
What do they mean

From the given, it is easy to show that ΔABC\displaystyle \Delta ABC is an equilateral triangle.
Hint: all its angle have the same measure.

Ok, I replied to the other comment as well. I am just not understanding the information they have given, like what the <DAB and <DCB mean exactly, so I am not sure how to use the information. Can you explain what those measurements are for?

Thanks. :)
 
Ok, I replied to the other comment as well. I am just not understanding the information they have given, like what the <DAB and <DCB mean exactly, so I am not sure how to use the information. Can you explain what those measurements are for?
Each refers to an angle in the picture.

\(\displaystyle \begin{align*}115^{\circ}-55^{\circ}&=60^{\circ} \\95^{\circ}-35^{\circ}&=60^{\circ}\\m(\angle B)&=60^{\circ}~~\text{WHY?} \end{align*}\)

Why does that make ΔABC an equilateral?
 
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