Answer:
Smaller angle = 36°
Larger angle = 144°
Explanation:
We can determine the measure of each angle using a system of equations, where:
- x represents the measure of one angle,
- and y represents the measure of the other angle.
First equation:
Since the sum of supplementary angles is always 180°, our first equation is given by:
x + y = 180
Second equation:
Since one angle measures four times the other, our second equation is given by:
x = 4y
Method to solve: Substitution:
Solving for y:
Now, we can find the measure of one angle by substituting x = 4y for x in the first equation:
4y + y = 180
(5y = 180) / 5
y = 36
Thus, one angle has a degree measure of 36°.
Solving for x:
Now we can find the measure of the other angle by plugging in 36 for y in the second equation:
x = 4(36)
x = 144
Thus, the other angle has a degree measure of 144°.