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 \(180^\circ\). One angle is \(90^\circ\) (right angle), another is \(48^\circ\), and the third is \(3x^\circ\). So, \(90 + 48 + 3x = 180\).

Step2: Simplify the equation

Add \(90\) and \(48\): \(138 + 3x = 180\).

Step3: Solve for \(x\)

Subtract \(138\) from both sides: \(3x = 180 - 138 = 42\). Then divide by \(3\): \(x = \frac{42}{3} = 14\).

Answer:

\(x = 14\)