Question

rs and vertical angles

Explanation:

Step1: Recall vertical - angles property

Vertical angles are equal. So, \(2m + 10=5m+100\).

Step2: Solve the equation for \(m\)

First, subtract \(2m\) from both sides: \(10 = 3m+100\). Then subtract 100 from both sides: \(- 90=3m\). Divide both sides by 3: \(m=-30\). But this seems wrong. Let's assume the correct equation is \(2m + 10+5m + 100=180\) (since they are linear - pair angles).

Step3: Combine like terms

\((2m+5m)+(10 + 100)=180\), which simplifies to \(7m+110 = 180\).

Step4: Solve for \(m\)

Subtract 110 from both sides: \(7m=180 - 110=70\). Divide both sides by 7: \(m = 10\).

Answer:

10