Question

the measures of the angles of a triangle are shown in the figure below. solve for x. the triangle has angles 80°, (5x+12)°, and 38°.

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\). So, \(80 + (5x + 12) + 38 = 180\).

Step2: Simplify the left side

Combine like terms: \(80 + 12 + 38 + 5x = 130 + 5x\). So, \(130 + 5x = 180\).

Step3: Solve for x

Subtract 130 from both sides: \(5x = 180 - 130 = 50\). Then divide by 5: \(x = \frac{50}{5} = 10\).

Answer:

\(x = 10\)