Show all your work and explain how you were able to find the measure of each angle including idenitifying the angle types for full credit.

First organize the information we are given according to the problem.

*Angle 1 and Angle 3 are congruent.

*Angle 4 and Angle 6 are congruent.

*Angle 3 and Angle 4 are complementary. This means that the measure of angle 3 plus the measure of angle 4 equals to 90.

Now knowing this:

Angle 3 is 26.5° because it is congruent to angle 1.

Angle 4 is 63.5° because by subtracting 26.5 from 90, you'll get the sum of 63.5. Once more, this is because angles 3 and 4 are complementary.

Angles 4, 5, and 6 are adjacent angles which form a straight line. Straight lines have an angle measure of 180°. So together, both angles 4 and 6 measure 127°. Knowing that a line is 180°, the measure of angle 5 needs to be 53°. You can check this once more by adding all the three numbers and getting 180°.