Question

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

Explanation:

Step1: Recall angle - sum property

The sum of the interior angles of a triangle is 180°. So, we have the equation \(82 + 57+x=180\).

Step2: Simplify the left - hand side

First, add 82 and 57: \(82 + 57=139\). The equation becomes \(139 + x=180\).

Step3: Solve for x

Subtract 139 from both sides of the equation: \(x=180 - 139\).
\(x = 41\)

Answer:

41