Let's tackle this question by understanding the properties of supplementary angles.
Supplementary Angles
Supplementary angles are a pair of angles that add up to 180 degrees. When two angles are supplementary, they form a straight line, and together, they create a straight angle.
Let's denote the measure of one angle as "x" degrees. According to the problem, the other angle is 40 degrees more than this angle, so the measure of the second angle can be represented as "x + 40" degrees.
Since supplementary angles add up to 180 degrees, we can set up the equation:
x + (x + 40) = 180
Now, solve for "x":
2x + 40 = 180
Subtract 40 from both sides:
2x = 140
Divide by 2:
x = 70
Now that we have the value of "x," which represents one angle, we can find the measure of the other angle:
Second angle = x + 40 = 70 + 40 = 110 degrees
Answer:
The two supplementary angles are 70 degrees and 110 degrees.