Question

the measures of the angles of a triangle are shown in the figure below. solve for x. (x+19)° 54° triangle with a right angle

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\). This triangle has a right angle (\(90^\circ\)), \(54^\circ\), and \((x + 19)^\circ\).

Step2: Set up the equation

So, \(90 + 54 + (x + 19) = 180\). Simplify the left side: \(90 + 54 = 144\), then \(144 + x + 19 = x + 163\). So the equation is \(x + 163 = 180\).

Step3: Solve for x

Subtract 163 from both sides: \(x = 180 - 163 = 17\).

Answer:

\(x = 17\)