Question

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

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. So, we have the equation \(33+(5x - 13)+90=180\).

Step2: Simplify the left - hand side of the equation

First, combine like terms: \(33-13 + 90+5x=180\). Then, \(20 + 90+5x=180\), which simplifies to \(110+5x=180\).

Step3: Isolate the variable term

Subtract 110 from both sides of the equation: \(5x=180 - 110\). So, \(5x=70\).

Step4: Solve for x

Divide both sides of the equation by 5: \(x=\frac{70}{5}\).

Answer:

\(x = 14\)