Question

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

Explanation:

Step1: Use the triangle - angle sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, we have the equation \(x + 109+28=180\).

Step2: Simplify the left - hand side of the equation

First, add \(109\) and \(28\): \(109 + 28=137\). Then the equation becomes \(x+137 = 180\).

Step3: Solve for \(x\)

Subtract \(137\) from both sides of the equation: \(x=180 - 137\).

Answer:

\(x = 43\)