Question

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in the figure, ( m angle 7 = 100 ^ { circ } ). find the measure of ( angle 9 ).
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Explanation:

Step1: Use the property of supplementary angles

Since \(\angle7\) and \(\angle9\) are supplementary angles (they form a linear - pair as the lines are parallel and cut by a transversal, and \(\angle7+\angle9 = 180^{\circ}\)).

Step2: Solve for \(\angle9\)

Given \(m\angle7=100^{\circ}\), then \(m\angle9=180^{\circ}-m\angle7\).
Substitute \(m\angle7 = 100^{\circ}\) into the formula: \(m\angle9=180 - 100\).

Answer:

\(80^{\circ}\)