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: Define supplementary - angle relationship

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

Step2: Define the difference relationship

We are given that \(|x - y| = 35^{\circ}\). Let's assume \(x>y\), so \(x - y=35^{\circ}\).

Step3: Solve the system of equations

We have the system \(

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

\). Add the two equations: \((x + y)+(x - y)=180 + 35\).
Simplify the left - hand side: \(x + y+x - y = 2x\), and the right - hand side is \(215\). So \(2x=215\), then \(x=\frac{215}{2}=107.5^{\circ}\).
Substitute \(x = 107.5^{\circ}\) into \(x + y=180^{\circ}\), we get \(107.5+y = 180\), then \(y=180 - 107.5=72.5^{\circ}\).

Answer:

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