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A non-symmetrical arrow point exists such that the angle of the back

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A non-symmetrical arrow point exists such that the angle of the back  [#permalink]

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New post 28 Aug 2017, 23:38
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A
B
C
D
E

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  15% (low)

Question Stats:

74% (00:50) correct 26% (00:46) wrong based on 84 sessions

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A non-symmetrical arrow point exists such that the angle of the back of the arrow point equals 105°, similar to the diagram above. What is the sum of internal angles a, b, and c?

A. 105°
B. 125°
C. 127.5°
D. 145°
E. 180°


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Re: A non-symmetrical arrow point exists such that the angle of the back  [#permalink]

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New post 29 Aug 2017, 07:15
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Let the Triangle be ABC . Join A and C . Let angle O = 105
Now angle A= x + a
and Angle C = y +c

Therefore triangle AOC = x+ 105 + y = 180
x + y = 75

Therefore in triangle ABC = x + a + b +c + y =180
as x + y = 75
therefore a + b + c = 105
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Re: A non-symmetrical arrow point exists such that the angle of the back  [#permalink]

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New post 29 Aug 2017, 07:50
Connect Point of angle A and angle C to form a triangle.

This also forms another smaller triangle with one angle as 105. The other two angles have to be 75.

Now you can notice that in the bigger triangle, sum of a , b, c will be 180 - 75 = 105. That's your answer - A
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Re: A non-symmetrical arrow point exists such that the angle of the back  [#permalink]

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New post 17 Dec 2017, 06:14
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Bunuel is there an easier way to answer this question ?
Re: A non-symmetrical arrow point exists such that the angle of the back &nbs [#permalink] 17 Dec 2017, 06:14
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