Right triangle upper P upper Q upper R is labeled as follows: Angle upper R is a right angle. Right

Question

Right triangles $P Q R$ and $S T U$ are similar, where $P$ corresponds to $S$ . If the measure of angle $Q$ is $18 degree$ , what is the measure of angle $S$ ?

Accepted Answer

Choice B is correct. In similar triangles, corresponding angles are congruent. It&rsquo;s given that right triangles P Q R and S T U 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&rsquo;s given that the measure of angle Q is 18 /mo> , so the measure of angle T is also 18 /mo> . Angle U is a right angle, so the measure of angle U is 90 /mo> . The sum of the measures of the interior angles of a triangle is 180 /mo> . Thus, the sum of the measures of the interior angles of triangle S T U 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 .

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