Question

find the measures of the labeled angles. (x + 116)° = □° (type a whole number).

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. So, \(5x=x + 116\).

Step2: Solve the equation for \(x\)

Subtract \(x\) from both sides: \(5x−x=x + 116−x\), which gives \(4x=116\). Then divide both sides by 4: \(x=\frac{116}{4}=29\).

Step3: Find the measure of \(x + 116\)

Substitute \(x = 29\) into \(x + 116\), we get \(29+116 = 145\).

Answer:

145