Question

The measure of an angle exceeds three times the measure of its supplement by 20 degrees. Find its measure.

(a) 90 deg
(b) 140 deg.
(c) 110 deg.
(d) 60 deg.

Answer 1

To find the angle, we set up the equation x = 3(180 - x) + 20 where x is the angle, since it exceeds three times its supplement by 20 degrees. Solving the equation, we find that the angle measures 140 degrees.

Step-by-step explanation:

The question asks to find the measure of an angle that exceeds three times the measure of its supplement by 20 degrees. To solve this, we can define the angle as x and its supplement will be 180 - x (since two supplementary angles add up to 180 degrees). The problem states that the angle is 20 degrees more than three times its supplement, so we can write the equation: x = 3(180 - x) + 20.

Now, we solve for x:

1. x = 540 - 3x + 20
2. 4x = 560
3. x = 140 degrees

Therefore, the measure of the angle is 140 degrees, which corresponds to option (b).