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.