Question

the ( mangle6=(11x + 8)^{circ} ) and ( mangle7=(12x - 4)^{circ} ) what is the measure of ( angle4 )? ( mangle4 = 40^{circ} ) ( mangle4 = 48^{circ} ) ( mangle4 = 132^{circ} ) ( mangle4 = 140^{circ} )

Explanation:

Step1: Find the value of \(x\)

Since \(\angle6\) and \(\angle7\) are supplementary (they form a linear pair), \(m\angle6 + m\angle7=180^{\circ}\).

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Step2: Calculate \(m\angle6\)

Substitute \(x = 12\) into \(m\angle6=(11x + 8)^{\circ}\)

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Step3: Use the property of parallel lines (alternate - interior angles)

\(\angle4\) and \(\angle6\) are congruent (alternate - interior angles for parallel lines \(wx\) and \(y\) cut by a transversal). So \(m\angle4=m\angle6\)

Answer:

\(m\angle4 = 140^{\circ}\) (the fourth option)