Question

find the value of the variable and the measure of each labeled angle.

Explanation:

Step1: Set the two angles equal

Since vertical - angles are equal, we set \(x + 16=5x-24\).

Step2: Solve for \(x\)

Subtract \(x\) from both sides: \(16 = 4x-24\). Then add 24 to both sides: \(40 = 4x\). Divide both sides by 4, so \(x = 10\).

Step3: Find the measure of \((x + 16)^{\circ}\)

Substitute \(x = 10\) into \(x + 16\), we get \(10+16=26\).

Step4: Find the measure of \((5x - 24)^{\circ}\)

Substitute \(x = 10\) into \(5x - 24\), we get \(5\times10-24=50 - 24=26\).

Answer:

\(x = 10\)
\((x + 16)^{\circ}=26^{\circ}\)
\((5x - 24)^{\circ}=26^{\circ}\)