Question

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

Explanation:

Step1: Recall the sum of angles in a triangle

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(49^{\circ}+34^{\circ}+x^{\circ}=180^{\circ}\).

Step2: Simplify the left - hand side

First, add \(49\) and \(34\): \(49 + 34=83\). The equation becomes \(83+x = 180\).

Step3: Solve for \(x\)

Subtract \(83\) from both sides of the equation: \(x=180 - 83\).

Answer:

\(x = 97\)