Two angles are complementary. The sum of the measures of the larger angle and three times the measure of the smaller angle is 114. What is the measure of each angle?

A + B = 90º (complementary)

Then A = 90º - B

A + 3B = 114º

Substitute 90º-B for e in second equation and solve for B. Insert that value into the first equation and solve for A. Check by inserting both values into the second equation.

To solve this question, we need to set up an equation based on the given information.

Let's assume that the measure of the smaller angle is x degrees. Since the two angles are complementary, the larger angle would be 90 - x degrees.

According to the problem, the sum of the measures of the larger angle (90 - x) and three times the measure of the smaller angle (3x) is 114.

So we can write the equation as:

(90 - x) + 3x = 114

Now, we can solve this equation to find the value of x, which represents the measure of the smaller angle.

90 - x + 3x = 114
90 + 2x = 114
2x = 114 - 90
2x = 24
x = 24/2
x = 12

Therefore, the measure of the smaller angle is 12 degrees.

To find the measure of the larger angle, we substitute the value of x back into 90 - x:

90 - 12 = 78

Therefore, the measure of the larger angle is 78 degrees.

So, the measure of each angle is 12 degrees and 78 degrees.