Question

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

Explanation:

Step1: Recall the triangle angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(58^{\circ}+39^{\circ}+x^{\circ}=180^{\circ}\).

Step2: Simplify the left - hand side

First, add \(58\) and \(39\): \(58 + 39=97\). The equation becomes \(97+x = 180\).

Step3: Solve for \(x\)

Subtract \(97\) from both sides of the equation: \(x=180 - 97\).

Answer:

\(x = 83\)