Two angles are complementary. The sum of the measure of the first angle and one-fourth of the second angle is 69 degrees. Find the measures of the angles.

What is the measure of the smaller angle?
What is the measure of the other angle?

Can somebody help me set this up?
PLEASE!!!!!!

A+B=90

A+ 1/4 B=69

"Two angles are complementary" ---> x + y = 90

"The sum of the measure of the first angle and one-fourth of the second angle is 69 degrees" ---> x + (1/4)y = 69
or
4x + y = 276
-----------------------------

4x + y = 276
x + y = 90

subtract them etc.

Certainly, I can help you set up and solve this problem step by step.

Let's say the first angle is represented by 'x' degrees.
And the second angle is represented by 'y' degrees.

Given that the two angles are complementary, we know that the sum of their measures is equal to 90 degrees. So we can set up the equation:

x + y = 90 ---(equation 1)

Now, let's consider the second condition given in the problem:
"The sum of the measure of the first angle and one-fourth of the second angle is 69 degrees."

The measure of the first angle is 'x' degrees, and one-fourth of the second angle is (1/4)*y degrees.

So we can set up another equation based on this information:

x + (1/4)*y = 69 ---(equation 2)

Now we have a system of two equations (equation 1 and equation 2) that we can solve simultaneously to find the values of 'x' and 'y'.

To solve this system, we can use a method called substitution or elimination. Let's use the substitution method.

From equation 1, we can express x in terms of y:

x = 90 - y

Now, we substitute this value of x in equation 2:

(90 - y) + (1/4)*y = 69

Simplifying the equation:

90 - y + (1/4)*y = 69
Multiply both sides of the equation by 4 to eliminate the fraction:
360 - 4y + y = 276
Combine like terms:
360 - 3y = 276
Subtract 360 from both sides:
-3y = -84
Divide both sides by -3:
y = 28

So, the measure of the second angle is 28 degrees.

To find the measure of the first angle, we can substitute this value of y into equation 1:

x + 28 = 90
Subtract 28 from both sides:
x = 62

Hence, the measure of the smaller angle (x) is 62 degrees, and the measure of the other angle (y) is 28 degrees.

Therefore, the smaller angle measures 62 degrees, and the other angle measures 28 degrees.