Question

the measures of the angles of a triangle are shown in the figure below. solve for x. 62° (5x - 8)° 36°

Explanation:

Step1: Use triangle angle - sum property

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(62^{\circ}+36^{\circ}+(5x - 8)^{\circ}=180^{\circ}\).

Step2: Simplify the left - hand side

First, combine the constant terms: \(62 + 36-8+5x=180\).
\(90+5x = 180\).

Step3: Solve for \(x\)

Subtract \(90\) from both sides: \(5x=180 - 90\).
\(5x = 90\).
Divide both sides by \(5\): \(x=\frac{90}{5}\).
\(x = 16\).

Answer:

\(x = 16\)