Question

find the measures of two supplementary angles if the difference between the measures of the two angles is 35. o a) 62.5°, 94.5° o b) 72.5°, 107.5° o c) 52°, 86.5° o d) 40°, 75°

Explanation:

Step1: Define variables for angles

Let the two supplementary angles be \( x \) and \( y \), where \( x > y \). Since they are supplementary, \( x + y = 180^\circ \). The difference between them is \( x - y = 35^\circ \).

Step2: 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: \( 2x = 215 \)
Solve for \( x \): \( x = \frac{215}{2} = 107.5^\circ \)

Substitute \( x = 107.5^\circ \) into \( x + y = 180 \): \( 107.5 + y = 180 \)
Solve for \( y \): \( y = 180 - 107.5 = 72.5^\circ \)

Answer:

B) \( 72.5^\circ, 107.5^\circ \)