Question

Find the value of X.

Answer 1

I used a somewhat unorthodox method for this but here goes...

First find the bottom left angle of the triangle which equals 180 - 108 because they are a linear pair and linear pairs always add to equal 180 degrees.  

Next I used the postulate that states "If two parralel lines are cut by a transversal, then there alternate interior angles are congruent".  The bottom right exterior angle of this triangle equals 4x, which means the other side of the transversal equals 4x as well.  I also know the exterior on the left side of the triangle excluding the vertex (x) equals 72, which we figured out in the first step.

4x = 72 + x

Next subtract x from both sides.

3x = 72

Then divide both sides by 3.

3/3 x = 72/3

And there's your answer.

x = 24

Hope this helps, sorry if it was a little confusing.