OG详解-OG4 数学1 Q9

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