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, \(45 + 57+x=180\).

Step2: Simplify the left - hand side of the equation

First, add \(45\) and \(57\): \(45 + 57=102\). The equation becomes \(102+x = 180\).

Step3: Solve for \(x\)

Subtract \(102\) from both sides of the equation: \(x=180 - 102\). Then \(x = 78\).

Answer:

\(78\)