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angle ABC and angle EBD are a pair of vertical angles; m angle ABC= 3x+8 and m angle EBF= 2x +48.  What are m angle ABC and m angle EBF?

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3 Answers

First, solve for x in the equation 3x + 8 = 2x + 48

Subracting 8 from both sides gives 3x = 2x + 40

Subracting 2x from both sides gives: 3x - 2x = 40, which simplifies to x = 40.

Plug x back into your equations.

Since ABC = 3x+8 and x = 40, ABC = 3*(40) + 8 = 120 + 8 = 128

Since EBF = 2x + 48 and x = 40, EBF = 2*(40) + 48 = 80 + 48 = 128

Both angles have the same value, as vertical angles do. :)

Wrong Question. Where did  point F come from? 

You said ABC and EBD are pair of verticle angles. And then question went on givin some new angle EBF , but we do not know where point F is? The way you gave the above question is not correct.

An interesting question where representation of the angles comes to play.

Vertical angles are formed if two lines intersect. Definition: A pair of non-adjacent angles formed by the intersection of two straight lines. They are opposite angles and are equal inmeasure. The adjacent angles add to 180.

David has given the solution above perfectly, I just wanted to add some theory into this thought.