the measure of an angle is 28 degrees greater than its complement. Find the measure of each angle.
x + x + 28 = 90
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90
To find the measure of each angle, let's first define what is meant by the "complement" of an angle.
In geometry, the complement of an angle is defined as the angle that, when added to the given angle, results in a 90-degree angle (a right angle).
Let's represent the given angle as x degrees, and its complement as y degrees.
According to the problem, the measure of the angle is 28 degrees greater than its complement. Mathematically, we can state this as:
x = y + 28
We also know that the sum of an angle and its complement is 90 degrees. So we can write another equation:
x + y = 90
Now, we have a system of equations with two variables (x and y). We can solve this system of equations to find the values of x and y.
Let's solve the system of equations using the substitution method:
From the first equation, we have x = y + 28. We can substitute this value of x into the second equation:
(y + 28) + y = 90
2y + 28 = 90
Subtract 28 from both sides:
2y = 62
Divide both sides by 2:
y = 31
Now we know the value of y, which is the complement of the angle. To find the measure of the angle (x), we substitute this value of y into the first equation:
x = y + 28
x = 31 + 28
x = 59
Therefore, the measure of the angle is 59 degrees, and its complement is 31 degrees.