Use an algebraic equation to find the measures of the two angles described below. Begin by letting x represent the degree measure of the angle's complement.
The measure of the angle is 76 degrees greater than its complement.
What is the angle of the complement?
x=?
What is the measure of the other angle?
x = (90 - x) + 76
2x = 166
x = 83
so the angle is 83 degrees and the complement is 7 degrees
Let x represent the degree measure of the angle's complement.
Since the measure of the angle is 76 degrees greater than its complement, the measure of the angle can be expressed as:
x + 76
To find the angle of the complement, we solve for x:
x = ?
To find the measure of the other angle, we substitute the value of x into the expression for the angle's measure:
x + 76
To solve this problem, we need to set up an equation based on the given information. Let's start by determining the degree measure of the complement angle.
We are told that the measure of the angle is 76 degrees greater than its complement. Since x represents the measure of the angle's complement, the measure of the angle itself can be written as x + 76.
Now we can set up an equation to represent the relationship between the angle and its complement:
Angle + Complement = 180 degrees (since they are complementary angles)
Substituting x + 76 for the measure of the angle and x for the measure of its complement, we get:
(x + 76) + x = 180
Combining like terms:
2x + 76 = 180
Next, we can simplify the equation:
2x = 180 - 76
2x = 104
Finally, to solve for x, we divide both sides of the equation by 2:
x = 104/2
x = 52
Therefore, the measure of the complement angle is 52 degrees.
To find the measure of the other angle, which is the angle itself, we substitute the value of x into the equation we found earlier:
Angle = x + 76
Angle = 52 + 76
Angle = 128
So, the measure of the other angle is 128 degrees.