Question

1. right triangle pqr is a dilation of triangle stu, where p corresponds to s and u is a right angle. if the measure of angle q is 38 degrees, what is the measure of angle s? 38 52 128 62

Explanation:

Step1: Use the property of similar triangles

Since triangle \(PQR\) is a dilation of triangle \(STU\), they are similar. In a right - triangle, the sum of the non - right angles is \(90^{\circ}\).

Step2: Calculate the measure of angle \(S\)

We know that in right - triangle \(PQR\), \(\angle Q = 38^{\circ}\) and \(\angle R = 90^{\circ}\). In right - triangle \(STU\), \(\angle U=90^{\circ}\). Using the angle - sum property of a triangle (\(\angle S+\angle T+\angle U = 180^{\circ}\)) and for similar triangles corresponding angles are equal. Also, \(\angle Q\) and \(\angle T\) are corresponding angles. So \(\angle S=90^{\circ}-\angle T\). Since \(\angle T=\angle Q = 38^{\circ}\), then \(\angle S=90 - 38\).

Answer:

\(52\)