Question

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

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\). This is a right triangle, so one angle is \(90^\circ\), another is \(26^\circ\), and the third is \(x^\circ\).

Step2: Set up the equation

Using the angle - sum property, we have the equation \(90 + 26+x=180\).

Step3: Solve for x

First, add \(90\) and \(26\): \(90 + 26=116\). Then the equation becomes \(116 + x=180\). Subtract \(116\) from both sides: \(x = 180-116\). Calculate \(180 - 116 = 64\).

Answer:

\(x = 64\)