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, \((7x - 8)+59 + 73=180\).

Step2: Simplify the left - hand side of the equation

First, combine the constant terms: \(7x-8 + 132=180\), which simplifies to \(7x+124 = 180\).

Step3: Solve for \(x\)

Subtract \(124\) from both sides: \(7x=180 - 124\), so \(7x = 56\). Then divide both sides by \(7\): \(x=\frac{56}{7}\).

Answer:

\(x = 8\)