Hi tysonrss,

What have you tried so far? This is pretty straight forward if you are familiar with a few geometric postulates and/or theorems.

[1a] When two parallel lines are cut by a transversal, alternate interior angles are congruent.

[1b]When two parallel lines are cut by a transversal, corresponding angles are congruent.

[2] Base angles of an isosceles triangle are congruent.

[3] Vertical angles are congruent

[4] Two angles that form a linear pair are supplementary

To get you started, angles 1 and 8 are congruent by [1a].

Angles 7 and 8 are congruent by [2]

Angles 7 and 2 are congruent by [1a]

Can you determine the rest?