Set 3: Polynomial Functions (Advanced)

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 angle 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 o , so the measure of angle T is also 18 o . Angle U is a right angle, so the measure of angle U is 90 o . The sum of the measures of the interior angles of a triangle is 180 o. 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. Choice C is incorrect. This is the measure of angle T . Choice D is incorrect and may result from conceptual or calculation errors. Choice A is incorrect. This is the sum of the measures of angle S and angle U .