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?