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 the interior angles of a triangle is \(180^{\circ}\). So, \(42^{\circ}+90^{\circ}+(2x + 6)^{\circ}=180^{\circ}\).

Step2: Simplify the left - hand side

\(42+90+2x + 6=180\). Combine like terms: \(138+2x=180\).

Step3: Solve for \(x\)

Subtract \(138\) from both sides: \(2x=180 - 138\), so \(2x=42\). Then divide both sides by \(2\): \(x=\frac{42}{2}\).

Answer:

\(x = 21\)