The measures of an angle and its complement differ by 22 degrees. What are the measures of the angles?
90 = 2x -22
68 = 2x
34 = x
One angle = 34 degrees
Other angle = 34 + 22 = ?
Well, let's call the measure of the angle x. The measure of its complement would be 90 degrees - x. According to the given information, the difference between the angle and its complement is 22 degrees. So, we can write the equation: x - (90 - x) = 22. Simplifying that, we get 2x - 90 = 22. Adding 90 to both sides, we have 2x = 112. Finally, dividing both sides by 2, we find that x = 56. Therefore, the angle measures 56 degrees and its complement measures 34 degrees.
Let's call the angle x.
The complement of an angle is the angle that, when added to the original angle, equals 90 degrees.
So, the complement of x is (90 - x) degrees.
We are given that the difference between the angle and its complement is 22 degrees.
Therefore, we can set up the equation:
x - (90 - x) = 22
Simplifying the equation, we get:
x - 90 + x = 22
2x - 90 = 22
2x = 112
x = 56
So the measure of the angle is 56 degrees.
To find the measure of its complement, we substitute this value into (90 - x):
90 - 56 = 34
Therefore, the measures of the angles are 56 degrees and 34 degrees.
To solve this problem, let's first understand the concept of complementary angles. Complementary angles are two angles that add up to 90 degrees.
Let's assume the measure of the angle we are trying to find is x degrees.
According to the problem, the measures of the angle and its complement differ by 22 degrees. Therefore, the measure of the complement angle would be (x + 22) degrees.
Since the sum of complementary angles is 90 degrees, we can set up the following equation:
x + (x + 22) = 90
Simplifying the equation, we have:
2x + 22 = 90
Next, we will isolate the variable x by subtracting 22 from both sides of the equation:
2x + 22 - 22 = 90 - 22
This simplifies to:
2x = 68
Finally, we solve for x by dividing both sides of the equation by 2:
2x/2 = 68/2
This simplifies to:
x = 34
Therefore, the measure of the angle is 34 degrees, and the measure of its complement is (34 + 22) = 56 degrees.