Question

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

Explanation:

Step1: Recall the triangle angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(48+(9x - 4)+73=180\).

Step2: Simplify the left - hand side of the equation

First, combine the constant terms: \(48-4 + 73+9x=180\). Then, \(44+73+9x=180\), and \(117+9x=180\).

Step3: Solve for \(x\)

Subtract \(117\) from both sides of the equation: \(9x=180 - 117\). So, \(9x=63\). Then divide both sides by \(9\): \(x=\frac{63}{9}\).

Answer:

\(x = 7\)