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 \(180^{\circ}\). Let the three angles of the triangle be \(x^{\circ}\), \(28^{\circ}\), and \(90^{\circ}\) (since there is a right - angle in the triangle).
So, we have the equation \(x + 28+90=180\).

Step2: Simplify the left - hand side of the equation

First, add \(28\) and \(90\): \(x+(28 + 90)=x + 118\).
The equation becomes \(x+118 = 180\).

Step3: Solve for \(x\)

Subtract \(118\) from both sides of the equation: \(x=180 - 118\).
\(x = 62\).

Answer:

\(62\)