Question

current skill
find the measure of angle 6.

Explanation:

Step1: Use the property of same - side exterior angles

Since the two lines are parallel, \(8x + 214\) and \(-2x+84\) are same - side exterior angles. And same - side exterior angles are supplementary, so \((8x + 214)+(-2x + 84)=180\).

$$\begin{align*} 8x+214-2x + 84&=180\\ 6x+298&=180\\ 6x&=180 - 298\\ 6x&=- 118\\ x&=-19.67 \end{align*}$$

Step2: Calculate the measure of \(\angle6\)

\(\angle6\) and \(8x + 214\) are supplementary (linear pair). First, substitute \(x = - 19.67\) into \(8x+214\): \(8\times(-19.67)+214=-157.36 + 214 = 56.64\). Then \(\angle6=180-(8x + 214)\).
Since \(8x+214 = 56.64\), \(\angle6=180 - 56.64=123.36\approx124\)

Answer:

\(124^{\circ}\)