Question

unit 3 - geometry question 9, 6.1.39 part 3 of 3 find the measures of angles x, y, and z in the figure. ∠y = 139° ∠x = 41° ∠z =

Explanation:

Step1: Use vertical - angles property

Vertical angles are equal. Since \(y\) and the given \(139^{\circ}\) angle are vertical angles, \(y = 139^{\circ}\).

Step2: Use linear - pair property

\(x\) and the \(139^{\circ}\) angle form a linear pair. A linear pair of angles sums to \(180^{\circ}\). So \(x=180 - 139=41^{\circ}\).

Step3: Use vertical - angles property for \(z\)

\(z\) and \(x\) are vertical angles. Since vertical angles are equal, \(z=x = 41^{\circ}\).

Answer:

\(z = 41^{\circ}\)