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 \(48^\circ\), and the third is \((5x + 17)^\circ\). So we set up the equation: \(90 + 48 + (5x + 17) = 180\).

Step2: Simplify the left side

First, add the constant terms: \(90 + 48 + 17 = 155\). So the equation becomes \(5x + 155 = 180\).

Step3: Solve for x

Subtract 155 from both sides: \(5x = 180 - 155 = 25\). Then divide both sides by 5: \(x = \frac{25}{5} = 5\).

Answer:

\(x = 5\)