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 property

The sum of the interior angles of a triangle is \(180^{\circ}\).

Step2: Set up the equation

We know one angle is \(90^{\circ}\) (right - angle), another is \(53^{\circ}\), and the third is \(x^{\circ}\). So, \(x+53 + 90=180\).

Step3: Simplify the left - hand side of the equation

\(x+(53 + 90)=x + 143\). The equation becomes \(x+143=180\).

Step4: Solve for \(x\)

Subtract \(143\) from both sides: \(x=180 - 143\).
\(x = 37\).

Answer:

\(x = 37\)