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For some value 'd', an isosceles triangle has at least one angle of

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For some value 'd', an isosceles triangle has at least one angle of  [#permalink]

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New post 19 May 2019, 01:55
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For some value 'd', an isosceles triangle has at least one angle of (2d-40) degrees and at least one angle of (d+20) degrees. For each of such triangles, let x denote the smallest angle in degrees. Then what is the sum of all possible x's?

A. 50
B. 56
C. 106
D. 126
E. 150
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Re: For some value 'd', an isosceles triangle has at least one angle of  [#permalink]

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New post 19 May 2019, 04:07
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nick1816 wrote:
For some value 'd', an isosceles triangle has at least one angle of (2d-40) degrees and at least one angle of (d+20) degrees. For each of such triangles, let x denote the smallest angle in degrees. Then what is the sum of all possible x's?

A. 50
B. 56
C. 106
D. 126
E. 150


Three cases


1) angle that is twice is 2d-40
So 2(2d-40)+d+20=180...5d=240.....d=48
So angles are 2d-40=2*48-40=56 and d+20=48+20=68..
Least angle or X is 56..
2) angle that is twice is d+20
So (2d-40)+2(d+20)=180...4d=180......d=45
So angles are 2d-40=2*45-40=50 and d+20=45+20=65.
Least angle or X is 50..
3) angle that is twice is 2d-40 and d+20
So (2d-40)=d+20......d=60.
So angles are 2d-40=2*60-40=80 and d+20=60+20=80, so third angle is 180-80-80=20
Least angle or X is 20.

Sum becomes 56+50+20=126

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Re: For some value 'd', an isosceles triangle has at least one angle of   [#permalink] 19 May 2019, 04:07
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