Question

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°

Explanation:

Step1: Set up equations

Let the two supplementary angles be $x$ and $y$ ($x>y$). Supplementary angles mean $x + y=180^{\circ}$, and the difference is $x - y = 35^{\circ}$.

Step2: Solve the system of equations

Add the two equations together: $(x + y)+(x - y)=180^{\circ}+ 35^{\circ}$. Simplifying gives $2x=215^{\circ}$, so $x = 107.5^{\circ}$.

Step3: Find the other angle

Substitute $x = 107.5^{\circ}$ into $x + y=180^{\circ}$, we get $107.5^{\circ}+y = 180^{\circ}$, then $y=180^{\circ}-107.5^{\circ}=72.5^{\circ}$.

Answer:

B. $72.5^{\circ}, 107.5^{\circ}$