Question

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

Explanation:

Step1: Recall angle - sum property

The sum of the interior angles of a triangle is 180°. So, we have the equation $65+(5x + 14)+36=180$.

Step2: Simplify the left - hand side

Combine like terms: $(65 + 14+36)+5x=180$, which gives $115 + 5x=180$.

Step3: Isolate the variable term

Subtract 115 from both sides of the equation: $5x=180 - 115$, so $5x=65$.

Step4: Solve for x

Divide both sides by 5: $x=\frac{65}{5}$.

Answer:

$x = 13$