Question

one of the angles of △abc has a measure of 57°. one of the angles of △rst has a measure of 83°. if △abc and △rst are similar, what is the measure of the smallest angle of △rst?

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\). For similar triangles, corresponding angles are equal.

Step2: Find the third angle in ABC (and RST)

Let the angles of \(\triangle ABC\) be \(57^\circ\), \(x\), \(y\) and of \(\triangle RST\) be \(83^\circ\), \(x\), \(y\) (since similar). First, find the third angle in a triangle with angles \(57^\circ\) and \(83^\circ\): \(180 - 57 - 83 = 40^\circ\).

Step3: Identify the smallest angle

Compare \(40^\circ\), \(57^\circ\), \(83^\circ\). The smallest is \(40^\circ\).

Answer:

\(40^\circ\)