Question

the measures of the angles of a triangle are shown in the figure below. solve for x.

Explanation:

Step1: Recall triangle angle sum

A triangle's angles sum to \(180^\circ\). This is a right triangle, so one angle is \(90^\circ\), another is \(24^\circ\), and the third is \(x^\circ\).

Step2: Set up the equation

\(90 + 24 + x = 180\)

Step3: Solve for x

First, add \(90\) and \(24\): \(90 + 24 = 114\). Then, subtract from \(180\): \(x = 180 - 114 = 66\).

Answer:

\(x = 66\)