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If the complement of a certain angle is three times...

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by BTGmoderatorLU » Wed Oct 25, 2017 3:49 pm
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°

The OA is C.

Can any expert explain this PS question for me please? I don't have it clear. Thanks.
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by EconomistGMATTutor » Wed Oct 25, 2017 4:14 pm
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°

The OA is C.

Can any expert explain this PS question for me please? I don't have it clear. Thanks.
Hi LUANDATO,
Let's take a look at your question.

We know that when two angles add to 90°, they are said to be complement of each other.
So, if a and b are complement of each other then,
$$a+b=90$$

The question states:
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?
Let the certain angle be 'x'.
Then,
$$x\ +\ 3x\ =\ 90°$$
$$4x=90°$$
$$x=\frac{90}{4}$$
$$x=22.5°$$

Therefore, Option C is correct.

Hope it helps.
I am available if you'd like any follow up.
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Re: If the complement of a certain angle is three times...

by Scott@TargetTestPrep » Sat Jan 18, 2020 4:41 am
BTGmoderatorLU wrote: ↑
Wed Oct 25, 2017 3:49 pm
 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°

The OA is C.

Can any expert explain this PS question for me please? I don't have it clear. Thanks.
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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