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# If the supplement of a certain angle is six times the measure of the

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Math Expert
Joined: 02 Sep 2009
Posts: 50009
If the supplement of a certain angle is six times the measure of the  [#permalink]

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28 Sep 2016, 02:53
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Difficulty:

35% (medium)

Question Stats:

66% (01:13) correct 34% (02:09) wrong based on 72 sessions

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

A. 36°
B. 50°
C. 56°
D. 60°
E. 72°

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Posts: 593
Re: If the supplement of a certain angle is six times the measure of the  [#permalink]

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28 Sep 2016, 03:52
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Bunuel wrote:
If the supplement of a certain angle is six times the measure of the complement of that certain angle, then what is the measure of that certain angle?

A. 36°
B. 50°
C. 56°
D. 60°
E. 72°

Note : If we have some angle as a , the supplement angle is (180 - a ) and the complement angle is (90 - a).

(180 - a) = 6 (90 - a)

Then (180 - a) = 540 - 6a

=> (6x - a) = 540 - 180

=> 5a= 360
=> a = 360/5 = 72.

IMO option E.
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Joined: 23 Jun 2016
Posts: 41
Re: If the supplement of a certain angle is six times the measure of the  [#permalink]

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28 Sep 2016, 16:27
Plug in numbers. Couple of this to keep in mind complimentary angle is 90-A so if we have an angle 50 the complementary would be 40 since 50+40=90. Supplementary angle is 180-A. So if an angle is 20 then the supplementary is 160. Supplementary cannot be greater than 180

Statement B:
If the angle is 50 then the complementary angle is 40 (90-50) and the supplementary angle = 240 (not possible the angle be greater than 50 )

Statement D:
If the angle is 60 then complimentary is 30 and supplementary = 180 not possible the angle must be larger 60

Answer E as the only option left

We can verify

Statement E if angle is 72 complimentary is 18 and supplementary = 108 (108+72= 180)
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Re: If the supplement of a certain angle is six times the measure of the  [#permalink]

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01 Mar 2017, 00:53
Let the angle be x.
Supplement angle = 180 - x.
Compliment angle = 90-x.
According to question 180-x = 6(90-x)
=> 5x = 360
=> x = 72
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Re: If the supplement of a certain angle is six times the measure of the  [#permalink]

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01 Mar 2017, 01:49
Bunuel wrote:
If the supplement of a certain angle is six times the measure of the complement of that certain angle, then what is the measure of that certain angle?

A. 36°
B. 50°
C. 56°
D. 60°
E. 72°

Simply note that the supplement would be 90 degrees more than the complement and this would account for 5 times the complement.
So the complementary angle would be 90/5 = 18 degrees

Hence that certain angle must be 90 - 18 = 72 degrees

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Re: If the supplement of a certain angle is six times the measure of the &nbs [#permalink] 01 Mar 2017, 01:49
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