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 property

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(39^{\circ}+62^{\circ}+(4x + 19)^{\circ}=180^{\circ}\).

Step2: Simplify the left - hand side of the equation

First, add the constant angles: \(39+62 + 19=120\). The equation becomes \(120+4x=180\).

Step3: Solve for \(x\)

Subtract \(120\) from both sides: \(4x=180 - 120\). So, \(4x=60\). Then divide both sides by \(4\): \(x=\frac{60}{4}\).

Answer:

\(x = 15\)