Question

in the figure, m∠7 = 100°. find the measure of ∠5.

Explanation:

Step1: Identify angle relationship

∠5 and ∠7 are same - side interior angles? No, wait, ∠5 and ∠7 are actually supplementary? Wait, no, looking at the transversal and parallel lines (assuming lines s, t, u are parallel and m is a transversal). Wait, ∠5 and ∠7: let's see, ∠5 and ∠7 are adjacent? No, ∠5 and ∠7, along with ∠6 and ∠8, form a linear pair? Wait, no, ∠5 and ∠7 are actually supplementary? Wait, no, ∠5 and ∠7: if we consider the transversal cutting the parallel lines, ∠5 and ∠7 are same - side interior angles? Wait, no, let's think again. ∠5 and ∠7: ∠5 and ∠7, when the transversal intersects the two lines (the lines with arrows, say line t and the other line), ∠5 and ∠7 are actually supplementary? Wait, no, ∠5 and ∠7 are vertical angles? No, ∠5 and ∠7: let's see, ∠5 and ∠7 are same - side interior angles? Wait, no, the sum of ∠5 and ∠7 should be 180 degrees because they are same - side interior angles (if the lines are parallel) or consecutive interior angles. Wait, the problem: we know that ∠5 and ∠7 are supplementary (they form a linear pair? Wait, no, ∠5, ∠6, ∠7, ∠8: ∠5 and ∠7 are vertical? No, ∠5 and ∠7: ∠5 + ∠7 = 180° because they are same - side interior angles or consecutive angles. Wait, the formula for supplementary angles is \(m\angle5 + m\angle7=180^{\circ}\) (if they are supplementary).

Step2: Solve for \(m\angle5\)

Given \(m\angle7 = 100^{\circ}\), we use the equation \(m\angle5=180^{\circ}-m\angle7\)
Substitute \(m\angle7 = 100^{\circ}\) into the equation: \(m\angle5 = 180^{\circ}- 100^{\circ}=80^{\circ}\)

Answer:

\(80^{\circ}\)