An angle measures 56° more than the measure of its supplementary angle. What is the measure of each angle?
17° and 73°
Let's assume the measure of the angle is x degrees.
The supplementary angle of x degrees will then be 180 - x degrees.
According to the given information, the angle measures 56 degrees more than its supplementary angle, which can be written as:
x = (180 - x) + 56
Simplifying the equation:
x = 180 + 56 - x
Combining like terms:
2x = 236
Dividing both sides by 2:
x = 236/2
x = 118
Therefore, the measure of the angle is 118 degrees, and its supplementary angle is 180 - 118 = 62 degrees.
To find the measure of each angle, we need to set up an equation based on the information given.
Let's assume the measure of one angle is x degrees. Its supplementary angle would be 180° - x (since the sum of supplementary angles is 180°).
According to the given information, the angle measures 56° more than its supplementary angle. This can be written as:
x = (180° - x) + 56°
Now, let's solve this equation to find the value of x:
x = 180° - x + 56°
2x = 180° + 56°
2x = 236°
x = 236° / 2
x = 118°
So, one angle measures 118°.
To find the measure of its supplementary angle, we substitute this value back into the equation:
180° - x = 180° - 118°
180° - x = 62°
Therefore, the measure of each angle is 118° and 62°.