Question

Find the value of x. Then find the measure of each labeled angle. don't mind the -2's, i got them wrong, these are test corrections.

Answer 1

Let's draw the triangles:

Since the lines with the red arrow are parallel, the angles in blue must be congruent because the triangles share the yellow angle (and the lines are parallel). Therefore, the angles in green are congruent too:

`3x-5=x+55`

So from here we can clear x:

`\begin{gathered} 3x-5=55+5 \\ 2x=60 \\ x=60/2 \\ x=30 \end{gathered}`

x = 30

And now we can find the measures of the labeled angles and verify that they are the same:

`\begin{gathered} 3x-5=3*30-5=90-5=85º \\ x+55=30+55=85º \end{gathered}`

The labeled angles are 85º