Question

the measures of the angles of a triangle are shown in the figure below. solve for x.
50°
70°
(6x - 18)°

Explanation:

Step1: Use the triangle - angle sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(50^{\circ}+70^{\circ}+(6x - 18)^{\circ}=180^{\circ}\).

Step2: Simplify the left - hand side of the equation

First, combine the constant terms: \(50 + 70-18+6x=180\). Then, \(102 + 6x=180\).

Step3: Solve for \(x\)

Subtract \(102\) from both sides: \(6x=180 - 102\). So, \(6x=78\). Divide both sides by \(6\): \(x=\frac{78}{6}\).

Answer:

\(x = 13\)