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Geometry and Trigonometry Difficulty: Medium

In triangle $A B C$ , the measure of angle $A$ is $54 degree$ , the measure of angle $B$ is $90 degree$ , and the measure of angle $C$ is $left parenthesis StartFraction k Over 2 EndFraction right parenthesis degree$ . What is the value of $k$ ?

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Explanation

Choice C is correct. The sum of the interior angles of a triangle is $180 degree$ . It's given that the interior angles of triangle $A B C$ are $54 degree$ , $90 degree$ , and $left parenthesis StartFraction k Over 2 EndFraction right parenthesis degree$ . It follows that $54 + 90 + \frac{k}{2} = 180$ , or $144 + \frac{k}{2} = 180$ . Subtracting $144$ from each side of this equation yields $\frac{k}{2} = 36$ . Multiplying each side of this equation by $2$ yields $k equals 72$ . Therefore, the value of $k$ is $72$ .

Choice A is incorrect. This is the value of $StartFraction k Over 2 EndFraction$ , not $k$ .

Choice B is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.