Question

If the difference of two supplementary angles is 30 degress, then find the angles.

• A. 30 degrees and 160 degrees
• B. 75 degrees and 105 degrees
• C. 25 degrees and 155 degrees
• D. 15 degrees and 165 degrees

Answer 1

The correct option is B 75 degrees and 105 degrees

When the sum of two angles is 180 degrees, then the angles are called supplementary angles.

Let one the angles measure x degrees.
So, the measure of the other angle = (180-x) degrees

Given, the difference of the two supplementary angles is 30 degress.

So,
(180-x) - x = 30 degrees
2x = 150 degrees
x = 75 degrees

So, (180-x) = (180-75) = 105 degrees