Right triangles PQR and STU are similar, where P corresponds to S. If the measure of angle Q is 18°,what is the measure of angle S ?

Explanation

Choice B is correct. In similar triangles, corresponding angles are congruent. It's given that right triangles PQR and STU are similar, where angle P corresponds to angle S. It follows that angle P is congruent to angle S. In the triangles shown, angle R and angie U are both marked as right angles, so angle R and angle U are corresponding angles. It follows that angle Q and angle T are corresponding angles, and thus, angle Q is congruent to angle T. It's given that the measure of angle Q is 18°, so the measure of angle T is also 18°. Angle U is a right angle, so the measure of angle U is 90°. The sum of the measures of the interior angles of a triangle is 180°. Thus, the sum of the measures of the interior angles of triangle STU is 180 degrees. Let s represent the measure, in degrees, of angle S. It follows that s + 18 + 90 = 180, or s + 108 =180. Subtracting 108 from both sides of this equation yields s = 72. Therefore, if the measure of angle Q is 18 degrees, then the measure of angle S is 72 degrees.