Question

in the figure, ( mangle 3 = 75^circ ) and ( mangle 10 = 105^circ ). find the measure of ( angle 9 ).

Explanation:

Step1: Use the property of supplementary angles

Supplementary angles add up to \(180^{\circ}\). We know that \(\angle3\) and \(\angle7\) are corresponding angles (assuming parallel lines and transversal). But more directly, \(\angle9\) and \(\angle10\) are supplementary.
The formula for supplementary angles is \(m\angle9 + m\angle10=180^{\circ}\)

Step2: Solve for \(m\angle9\)

Given \(m\angle10 = 105^{\circ}\), substitute into the formula:
\(m\angle9=180^{\circ}-m\angle10\)
\(m\angle9 = 180^{\circ}- 105^{\circ}\)
\(m\angle9=75^{\circ}\)

Answer:

\(75^{\circ}\)