Question

in \\( \triangle x y z \\), the measure of \\( \angle x \\) is \\( 24 ^ { \circ } \\) and the measure of \\( \angle y \\) is \\( 98 ^ { \circ } \\). what is the measure of \\( \angle z \\)?
\\( 212 ^ { \circ } \\)
\\( 122 ^ { \circ } \\)
\\( 74 ^ { \circ } \\)
\\( 58 ^ { \circ } \\)
clear my selection

Explanation:

Step1: Recall the sum of angles in a triangle

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(\angle X+\angle Y +\angle Z=180^{\circ}\).

Step2: Substitute the given values

We know \(\angle X = 24^{\circ}\) and \(\angle Y=98^{\circ}\). Substituting into the formula: \(24^{\circ}+98^{\circ}+\angle Z = 180^{\circ}\).

Step3: Solve for \(\angle Z\)

First, calculate \(24 + 98=122\). Then the equation becomes \(122^{\circ}+\angle Z=180^{\circ}\). Subtract \(122^{\circ}\) from both sides: \(\angle Z=180^{\circ}- 122^{\circ}\).

Answer:

\(58^{\circ}\)