105k views
5 votes
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°)

1 Answer

3 votes

Final answer:

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.

User Leif Neland
by
7.9k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories