Question

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

Explanation:

Step1: Recall angle - sum property

The sum of the interior angles of a triangle is 180°.

Step2: Set up equation

We know one angle is 42° and another is 90° (the right - angle), and the third is \(x\). So, \(42 + 90+x=180\).

Step3: Simplify the left - hand side

\(132 + x=180\).

Step4: Solve for \(x\)

Subtract 132 from both sides: \(x=180 - 132\).
\(x = 48\)

Answer:

48