Understanding Supplementary Angles
Supplementary angles are two angles whose measures add up to 180 degrees. For instance, if one angle measures "x" degrees, its supplement will measure "180 - x" degrees.
Problem Breakdown
We need to find an angle, let’s denote it as "x", that is 35 degrees less than its supplement.
Formulating the Equation
1. The supplement of angle "x" is:
180 - x
2. According to the problem, we can express this relationship as:
x = (180 - x) - 35
Solving the Equation
Now, let's simplify the equation:
1. Rewrite the equation:
x = 180 - x - 35
2. Combine like terms:
x + x = 180 - 35
2x = 145
3. Divide by 2:
x = 72.5
Conclusion
The measure of the angle is 72.5 degrees.
Verification
To confirm, we can find the supplement of 72.5 degrees:
- Supplement = 180 - 72.5 = 107.5 degrees
Now, check if it is indeed 35 degrees more:
- 107.5 - 72.5 = 35 degrees
This confirms that our solution is correct. The angle whose measure is 35 less than its supplement is 72.5 degrees.