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°.
