Find the measure of angle 1 given the following: angle 3 and angle 4 are complementary (angles add up to 90 degrees), angle 2 is congruent to angle 3, the measure of angle 2 is equal to 6x+24, and the measure of angle 4 is equal to 5x.

When you add up all the angles, it would be equal to 180 degrees.

Since angles 2 and 3 are congruent, angle 3 is also equal to 6x + 24.
We know also that angles 3 and 4 are complementary, so (6x+24) + 5x = 90. 

Let's find x. 
6x+24+5x = 90
11x = 90-24
11x = 66
x = 6

Angle 2 and 3 are 6(6) + 24 = 60 degrees
Angle 4 is 5(6) = 30 degrees 

180 - 60 - 60 - 30 = 30 degrees

Angle 1 is equal to 30 degrees :D :D