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Question

Let k be the ratio of the supplement of an acute angle to that of its complement. Then, k always satisfy which of the following conditions?

A
0<k<12
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B
12<k<1
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C
1 < k < 2
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D
k > 2
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Solution

The correct option is D k > 2
Let the acute angle be x.
Thus, the supplement of x is (180° – x) and the complement of x is (90° – x).
Since k is the ratio of supplement of an angle to its complement.
k=180x90x
=180x+xx90x
=1802x+x90x
=2(90x)+x90x
=2+x90x
k>2 (0<x<90)
Hence, the correct answer is option (d).

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