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 can write the equation: $106^{\circ}+45^{\circ}+(2x - 9)^{\circ}=180^{\circ}$.

Step2: Combine like - terms on the left - hand side

First, add the non - variable angle measures: $106 + 45-9=142$. The equation becomes $142+2x=180$.

Step3: Isolate the variable term

Subtract 142 from both sides of the equation: $2x=180 - 142$. So, $2x = 38$.

Step4: Solve for x

Divide both sides of the equation by 2: $x=\frac{38}{2}$.

Answer:

$x = 19$