Question

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

Explanation:

Step1: Use triangle angle sum property

The sum of angles in a triangle is \(180^{\circ}\). In a right - angled triangle, one angle is \(90^{\circ}\). So, \(30+(6x + 18)+90=180\).

Step2: Simplify the equation

Combine like terms: \(6x+30 + 18+90=180\), which simplifies to \(6x+138 = 180\).

Step3: Solve for \(x\)

Subtract \(138\) from both sides: \(6x=180 - 138\), so \(6x = 42\). Then divide both sides by \(6\): \(x=\frac{42}{6}\).

Answer:

\(x = 7\)