Question

Two angles are supplementary. The larger angle is 70 degrees larger than the smaller angle. Find the measure of both angles.

Answer 1

The smaller angle measures 55 degrees, and the larger angle measures 125 degrees. They are supplementary angles with the larger angle being 70 degrees greater than the smaller angle.

Step-by-step explanation:

To solve this problem, we will use the definition of supplementary angles: two angles that add up to 180 degrees. Let's denote the smaller angle as x and the larger angle as x + 70 since the larger angle is 70 degrees larger than the smaller one.

Now, we set up our equation based on the definition of supplementary angles:

x + (x + 70) = 180

Simplifying this, we get:

2x + 70 = 180

Then, we solve for x:

2x = 110

x = 55

So, the smaller angle is 55 degrees. To find the larger angle, we add 70 to the smaller angle:

55 + 70 = 125

Therefore, the larger angle is 125 degrees.

The main answer is that the smaller angle measures 55 degrees and the larger angle measures 125 degrees.