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If the complement of a certain angle is three times the measure of tha

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If the complement of a certain angle is three times the measure of tha  [#permalink]

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New post 11 Jul 2016, 13:35
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Question Stats:

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If the complement of a certain angle is three times the measure of that certain angle, then what is the measure of that certain angle?

A. 45°

B. 30°

C. 22.5°

D. 18°

E. 15°
Magoosh GMAT Instructor
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If the complement of a certain angle is three times the measure of tha  [#permalink]

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New post 11 Jul 2016, 14:06
1
alpham wrote:
If the complement of a certain angle is three times the measure of that certain angle, then what is the measure of that certain angle?

A. 45°

B. 30°

C. 22.5°

D. 18°

E. 15°

Dear alpham
I'm happy to respond. :-)

The source of this question is not clear to me, but I don't believe the question writers are very familiar with the GMAT. To the best of my knowledge, the word "complement" does not appear in the OG or any official materials. Yes, it's a valid word in the context of high school geometry, but this suggests that the question was written by someone who knows a lot about high school math but not a lot about the GMAT. Apparently, someone was trying to create a challenging question by using terminology that doesn't appear on the GMAT: this is typical of low quality GMAT practice Quant questions.

The complement of angle A is the angle which, when added to angle A, gives 90 degrees. The two acute angles of a right triangle are complements, for example.

The original angle is x, so the complement is 3x, and together, these add up to 90 degrees.

x + 3x = 90

4x = 90

x = 22.5°

Answer = (C)

Here's a high quality GMAT practice question:
repeated angles in nested triangles

Does this make sense?
Mike :-)
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Magoosh Test Prep


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Re: If the complement of a certain angle is three times the measure of tha  [#permalink]

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New post 23 Jan 2020, 11:40
1
alpham wrote:
If the complement of a certain angle is three times the measure of that certain angle, then what is the measure of that certain angle?

A. 45°

B. 30°

C. 22.5°

D. 18°

E. 15°


Recall that complementary angles add to 90 degrees. If we let x = the angle, we see that its complement is 90 - x, and the measure of that complement is 3x. Thus, we can create the equation:

3x = 90 - x

3x + x = 90

4x = 90

x = 90/4 = 45/2 = 22.5 degrees

Answer: C
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Re: If the complement of a certain angle is three times the measure of tha   [#permalink] 23 Jan 2020, 11:40
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