Question

given that the measure of ∠x is 60°, and the measure of ∠y is 90°, find the measure of ∠z. °

Explanation:

Step1: Recall angle sum on a straight line

Angles on a straight line sum to \(180^\circ\). So \( \angle x + \angle y + \angle z = 180^\circ \).

Step2: Substitute known values

We know \( \angle x = 60^\circ \), \( \angle y = 90^\circ \). Substitute into the equation: \( 60^\circ + 90^\circ + \angle z = 180^\circ \).

Step3: Solve for \( \angle z \)

Simplify left side: \( 150^\circ + \angle z = 180^\circ \). Subtract \( 150^\circ \) from both sides: \( \angle z = 180^\circ - 150^\circ = 30^\circ \).

Answer:

\( 30 \)