Question

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

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\). So, \(62^\circ + 82^\circ + (x + 12)^\circ = 180^\circ\).

Step2: Simplify the left side

Calculate \(62 + 82 + 12 = 156\), so the equation becomes \(x + 156 = 180\).

Step3: Solve for x

Subtract 156 from both sides: \(x = 180 - 156 = 24\).

Answer:

\(x = 24\)