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, \((9x - 4)+48 + 73=180\).

Step2: Simplify the left - hand side of the equation

First, combine the constant terms: \((9x-4)+(48 + 73)=9x-4 + 121=9x+117\).
The equation becomes \(9x+117 = 180\).

Step3: Solve for \(x\)

Subtract \(117\) from both sides: \(9x=180 - 117\), so \(9x=63\).
Divide both sides by \(9\): \(x=\frac{63}{9}\).

Answer:

\(x = 7\)