Question

1. m∠def_____

Explanation:

Step1: Set up the equation

Since the two - angles are vertical angles and vertical angles are equal, we set \(8x - 34=5x - 2\).
\[8x-34 = 5x - 2\]

Step2: Solve for \(x\)

Subtract \(5x\) from both sides: \(8x-5x-34=5x - 5x-2\), which simplifies to \(3x-34=-2\). Then add 34 to both sides: \(3x-34 + 34=-2 + 34\), so \(3x=32\), and \(x=\frac{32}{3}\).

Step3: Find the measure of \(\angle DEF\)

Substitute \(x = \frac{32}{3}\) into the expression for \(\angle DEF=(5x - 2)\).
\[m\angle DEF=5\times\frac{32}{3}-2=\frac{160}{3}-2=\frac{160 - 6}{3}=\frac{154}{3}\approx51.33^{\circ}\]

Answer:

\(\frac{154}{3}^{\circ}\)