Question

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

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. So, \(x + 4x+65^{\circ}=180^{\circ}\).

Step2: Combine like - terms

\(5x+65^{\circ}=180^{\circ}\).

Step3: Isolate the variable term

Subtract 65° from both sides: \(5x=180^{\circ}- 65^{\circ}\), so \(5x = 115^{\circ}\).

Step4: Solve for x

Divide both sides by 5: \(x=\frac{115^{\circ}}{5}=23^{\circ}\).

Answer:

\(x = 23^{\circ}\)