Question

solve for the value of r.
(diagram shows two intersecting lines with angles ((5r + 8)^circ) and ((7r - 8)^circ) marked)

Explanation:

Step1: Identify vertical angles

The two angles \((5r + 8)^\circ\) and \((7r - 8)^\circ\) are vertical angles, so they are equal.
\[5r + 8 = 7r - 8\]

Step2: Solve for \(r\)

Subtract \(5r\) from both sides:
\[8 = 2r - 8\]
Add 8 to both sides:
\[16 = 2r\]
Divide both sides by 2:
\[r = 8\]

Answer:

\(r = 8\)