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, \(81^{\circ}+55^{\circ}+(6x + 20)^{\circ}=180^{\circ}\).

Step2: Simplify the left - hand side of the equation

First, add the constant terms: \(81 + 55+20=156\). The equation becomes \(156+6x=180\).

Step3: Solve for \(x\)

Subtract \(156\) from both sides: \(6x=180 - 156\). So, \(6x=24\). Then divide both sides by \(6\): \(x=\frac{24}{6}\).

Answer:

\(x = 4\)