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, \(62^{\circ}+78^{\circ}+(2x - 4)^{\circ}=180^{\circ}\).

Step2: Simplify the left - hand side

First, add the known angles: \(62 + 78+(2x-4)=140+(2x - 4)\). Then, \(140+(2x - 4)=2x+136\). So, \(2x + 136=180\).

Step3: Solve for \(x\)

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

Answer:

\(x = 22\)