Question

The measure of the supplement of an angle is 20 degrees less than 4 times the measure of the angle. Find the measures of the two angles.

a. (15°, 43°)
b. (20°, 38°)
c. (24°, 34°)
d. (36°, 12°)

Answer 1

After setting up a system of equations based on the relationship between the two angles, it is found that the smaller angle is 40° and its supplement is 140°. However, this correct pair of angles does not match any of the answer choices provided in the question.

Step-by-step explanation:

The question asks us to find two angles where one angle is the supplement of the other and the measure of the supplement is 20 degrees less than 4 times the measure of the smaller angle. We declare two variables: let angle A be the measure of the smaller angle, and angle B be the measure of its supplement. According to the properties of supplementary angles, A + B = 180° (since supplementary angles add up to 180 degrees).

According to the problem statement, we also have that B = 4A - 20°. We can now set up a system of equations and solve for A:

1. A + B = 180°
2. B = 4A - 20°

We substitute the second equation into the first:

1. A + (4A - 20°) = 180°
2. 5A - 20° = 180°
3. 5A = 200°
4. A = 40°

Now that we have the measure of angle A, we can find the measure of B by plugging A back into the second equation:

1. B = 4(40°) - 20°
2. B = 160° - 20°
3. B = 140°

Therefore, the two angles are A = 40° and B = 140°. This was not one of the answer choices provided, indicating there may have been an error in the question or the provided choices.