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, \((2x + 16)^{\circ}+48^{\circ}+90^{\circ}=180^{\circ}\).

Step2: Combine like - terms

First, add the constant terms on the left - hand side: \(2x+16 + 48+90=2x + 154\). So, \(2x+154 = 180\).

Step3: Isolate the variable term

Subtract 154 from both sides of the equation: \(2x=180 - 154\), which gives \(2x = 26\).

Step4: Solve for x

Divide both sides of the equation by 2: \(x=\frac{26}{2}=13\).

Answer:

13