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, \((3x - 12)+60 + 90=180\).

Step2: Simplify the left - hand side of the equation

First, combine the constant terms: \(3x-12 + 150=180\), which simplifies to \(3x+138 = 180\).

Step3: Isolate the term with \(x\)

Subtract \(138\) from both sides of the equation: \(3x=180 - 138\), so \(3x=42\).

Step4: Solve for \(x\)

Divide both sides by \(3\): \(x=\frac{42}{3}\).

Answer:

\(x = 14\)