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

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BTGmoderatorLU: Moderator; Posts: 2505; Joined: Sun Oct 15, 2017 1:50 pm; Followed by:6 members

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

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. 45Â°

B. 30Â°

C. 22.5Â°

D. 18Â°

E. 15Â°

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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Source: Beat The GMAT — Problem Solving | Wed Oct 25, 2017 3:49 pm

EconomistGMATTutor: GMAT Instructor; Posts: 555; Joined: Wed Oct 04, 2017 4:18 pm; Thanked: 180 times; Followed by:12 members

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. 45Â°

B. 30Â°

C. 22.5Â°

D. 18Â°

E. 15Â°

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 90Â°, 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,
$$x\ +\ 3x\ =\ 90Â°$$
$$4x=90Â°$$
$$x=\frac{90}{4}$$
$$x=22.5Â°$$

Therefore, Option C is correct.

Hope it helps.
I am available if you'd like any follow up.

GMAT Prep From The Economist
We offer 70+ point score improvement money back guarantee.
Our average student improves 98 points.

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GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8083; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

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. 45Â°

B. 30Â°

C. 22.5Â°

D. 18Â°

E. 15Â°

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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