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, \(62 + 78 + (2x - 4) = 180\).

Step2: Simplify the left side

Calculate \(62 + 78 = 140\), then the equation becomes \(140 + 2x - 4 = 180\). Simplify further: \(136 + 2x = 180\).

Step3: Solve for x

Subtract 136 from both sides: \(2x = 180 - 136 = 44\). Divide by 2: \(x = \frac{44}{2} = 22\).

Answer:

\(x = 22\)