Question

linear pairs and vertical angles
what is the value of m?
image of intersecting lines with angles (2m + 10)° and (5m + 100)°, and multiple - choice options 30, 150, 70, 10

Explanation:

Step1: Identify angle relationship

The angles \((2m + 10)^\circ\) and \((5m + 100)^\circ\) are supplementary (linear pair), so their sum is \(180^\circ\).
\((2m + 10) + (5m + 100) = 180\)

Step2: Solve for \(m\)

Combine like terms: \(7m + 110 = 180\)
Subtract 110: \(7m = 70\)
Divide by 7: \(m = 10\)

Answer:

\(m = 10\)