I need help with this question.
"The measure of the supplement of an angle is 60 less than three times the measure of the complement of the angle.find the measure of the angle".
Please help!!!!
still no help
Thanks!!!
sus
To solve this question, let's break it down step by step.
1. Let's start by assigning variables to the unknowns:
- Let "x" be the measure of the angle.
- Let "s" be the supplement of the angle.
- Let "c" be the complement of the angle.
2. We can establish the relationships between the angle, its supplement, and its complement:
- The supplement of an angle is the sum of the angle and 180 degrees. So, we have:
s = x + 180 (Equation 1)
- The complement of an angle is the difference between 90 degrees and the angle. So, we have:
c = 90 - x (Equation 2)
3. The problem states that the measure of the supplement of the angle is 60 less than three times the measure of the complement of the angle. Translating this into an equation, we get:
s = 3c - 60 (Equation 3)
4. We can substitute equations 1 and 2 into equation 3, using the values we found for the supplement and the complement:
x + 180 = 3(90 - x) - 60
5. Simplify and solve the equation:
x + 180 = 270 - 3x - 60
x + 180 = 210 - 3x
4x + 180 = 210
4x = 210 - 180
4x = 30
x = 30/4
x = 7.5
Therefore, the measure of the angle is 7.5 degrees.
180 ° - x = 3 * ( 90 ° - x ) - 60 °
180 ° - x = 270 ° - 3 x - 60 °
180 ° - x = 210 ° - 3 x
- x + 3 x = 210 ° - 180 °
2 x = 30 ° Divide both sides by 2
x = 15 °