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: Recall the property of supplementary angles

Supplementary angles sum to \(180^{\circ}\). Let the two angles be \(x\) and \(y\), so \(x + y=180^{\circ}\).

Step2: Use the given difference

Given \(|x - y| = 35^{\circ}\). Assume \(x>y\), then \(x - y=35^{\circ}\).

Step3: Solve the system of equations

We have the system \(

$$\begin{cases}x + y=180\\x - y=35\end{cases}$$

\). Add the two equations: \((x + y)+(x - y)=180 + 35\), \(2x=215\), \(x = 107.5^{\circ}\). Substitute \(x = 107.5^{\circ}\) into \(x + y=180^{\circ}\), \(107.5+y=180\), \(y=180 - 107.5=72.5^{\circ}\).

Answer:

B. \(72.5^{\circ},107.5^{\circ}\)