Question

lines wy, mp, and gr, where ( mangle ybd=(2x + 0.6)^{circ},mangle mbn=(5x + 7)^{circ} ), and ( mangle xcd=(9x - 28.8)^{circ} ) are shown. determine the value of ( x ) that will show ( overline{wy}paralleloverline{gr} ). write your answer as a decimal and if necessary, round your answer to the nearest tenth.

Explanation:

Step1: Use vertical angles and corresponding angles

Since \( \angle MBN\) and \( \angle YBD\) are vertical angles, \(m\angle MBN=m\angle YBD\). And if \( \overline{WY}\parallel\overline{GR}\), then \(m\angle YBD = m\angle XCD\) (corresponding angles). So \(2x + 0.6=9x-28.8\)

Step2: Solve the equation for \(x\)

Subtract \(2x\) from both sides:
\(0.6=9x - 2x-28.8\)
\(0.6 = 7x-28.8\)
Add \(28.8\) to both sides:
\(0.6+28.8=7x\)
\(29.4 = 7x\)
Divide both sides by \(7\):
\(x=\frac{29.4}{7}\)

Answer:

\(4.2\)