The measure of one of two complementary angles is 21 less than twice the measure of the other angle. Find the measure of each angle

Let's assume that one angle is represented by x.

According to the problem, the other angle will be represented by 2x - 21.

Since the angles are complementary, their sum will be equal to 90 degrees.

So, we can set up the following equation:

x + (2x - 21) = 90

Now, let's solve for x:

3x - 21 = 90

Adding 21 to both sides of the equation:

3x = 111

Dividing both sides of the equation by 3:

x = 37

Therefore, one angle measures 37 degrees, and the other angle measures:

2x - 21 = 2(37) - 21 = 74 - 21 = 53 degrees.

So, the two angles are 37 degrees and 53 degrees.

Let's denote one of the two complementary angles as x, and the other angle as y.

According to the given information, we have the following equation: "The measure of one of two complementary angles is 21 less than twice the measure of the other angle."

Translation of the statement into an equation:
x = 2y - 21

Now, we know that two angles are complementary when their sum is equal to 90 degrees.
So, we can write the second equation as:
x + y = 90

Now, we have a system of two equations:
x = 2y - 21 (Equation 1)
x + y = 90 (Equation 2)

To find the values of x and y, we can solve this system of equations.

First, we can solve Equation 2 for y:
y = 90 - x

Next, substitute this value of y into Equation 1:
x = 2(90 - x) - 21

Now, solve for x:

x = 180 - 2x - 21
x + 2x = 180 - 21
3x = 159
x = 53

Substitute this value back into Equation 2 to find y:
53 + y = 90
y = 90 - 53
y = 37

Therefore, the measure of one angle is 53 degrees, and the other angle is 37 degrees.

x is measure of one angle

2x-21 is measure of other

x+2x-21=90
3x-21=90
3x=111
you go from here