120k views
4 votes
Find the measures of two supplementary angles if the difference between the measures of the two angles is 35°.

a. 62.5°, 94.5°
b. 72.5°, 107.5°
c. 52°, 86.5°
d. 40°, 75°

User MPaul
by
8.9k points

1 Answer

4 votes

Final answer:

To calculate the measures of two supplementary angles with a difference of 35°, we set up an equation using the sum of supplementary angles (180°) and solve for the smaller angle (72.5°). The larger angle is then calculated to be 107.5°, making the angle pair b. 72.5°, 107.5°.

Step-by-step explanation:

To find the measures of two supplementary angles when their difference is 35°, we must remember that the sum of supplementary angles is 180°. Let's denote the smaller angle by x and the larger angle will then be x + 35°. Writing the equation for their sum, we have:

x + (x + 35°) = 180°

This simplifies to:

2x + 35° = 180°

To solve for x, subtract 35° from both sides:

2x = 145°

Now, divide by 2:

x = 72.5°

Given that the difference between the angles is 35°, the other angle is:

x + 35° = 72.5° + 35°

= 107.5°

Therefore, the measures of the two supplementary angles are 72.5° and 107.5°, which corresponds to option b.

User CletusW
by
8.2k points