Question

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 $37+(4x + 6)+65=180$.

Step2: Simplify the left - hand side

Combine like terms: $(37 + 6+65)+4x=180$, which gives $108 + 4x=180$.

Step3: Isolate the variable term

Subtract 108 from both sides of the equation: $4x=180 - 108$, so $4x=72$.

Step4: Solve for x

Divide both sides by 4: $x=\frac{72}{4}=18$.

Answer:

$x = 18$