Question

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

Explanation:

Step1: Recall the sum of angles in a triangle

The sum of the interior angles of a triangle is \(180^{\circ}\).

Step2: Set up the equation

We have a right - angled triangle (one angle is \(90^{\circ}\)), another angle is \(57^{\circ}\), and the third angle is \(x^{\circ}\). So, \(x + 57+90=180\).

Step3: Solve the equation for \(x\)

Simplify the left - hand side: \(x + 147=180\). Then, subtract \(147\) from both sides: \(x=180 - 147\). So, \(x = 33\).

Answer:

\(x = 33\)