Question

topic 4: angle measures 19. if m∠def = 117°, find the value of x.

Explanation:

Step1: Set up the angle sum equation

The measure of \(\angle DEF\) is the sum of the measures of \(\angle DEG\) and \(\angle GEF\). So we have the equation: \((12x + 1) + (5x - 3) = 117\).

Step2: Combine like terms

Combine the \(x\)-terms and the constant terms: \(12x + 5x + 1 - 3 = 117\), which simplifies to \(17x - 2 = 117\).

Step3: Solve for \(x\)

Add 2 to both sides of the equation: \(17x - 2 + 2 = 117 + 2\), so \(17x = 119\). Then divide both sides by 17: \(x=\frac{119}{17}\).

Step4: Simplify the result

\(\frac{119}{17} = 7\).

Answer:

\(x = 7\)