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 parallel - line angle relationships

When \(\overline{WY}\parallel\overline{GR}\), by the property of parallel lines and transversals (corresponding angles and vertical angles), \(m\angle YBD + m\angle MBN=m\angle XCD\).
Substitute the given angle expressions: \((2x + 0.6)+(5x + 7)=9x-28.8\).

Step2: Simplify the left - hand side of the equation

Combine like terms on the left - hand side: \(2x+5x + 0.6 + 7=9x-28.8\), which gives \(7x+7.6 = 9x-28.8\).

Step3: Solve for \(x\)

Subtract \(7x\) from both sides: \(7x - 7x+7.6=9x-7x - 28.8\), so \(7.6 = 2x-28.8\).
Add \(28.8\) to both sides: \(7.6+28.8=2x-28.8 + 28.8\), then \(36.4 = 2x\).
Divide both sides by \(2\): \(x=\frac{36.4}{2}\).

Answer:

\(x = 18.2\)