Question

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

Explanation:

Step1: Use the triangle angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(37^{\circ}+65^{\circ}+(4x + 6)^{\circ}=180^{\circ}\).

Step2: Simplify the left - hand side of the equation

First, add the constant angles: \(37+65 + 6=108\). The equation becomes \(108+4x=180\).

Step3: Solve for \(x\)

Subtract \(108\) from both sides: \(4x=180 - 108\). So, \(4x=72\). Then divide both sides by \(4\): \(x=\frac{72}{4}\).

Answer:

\(x = 18\)