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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, 22:38
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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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[Reveal] Spoiler: OA

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Kudos [?]: 135833 [0], given: 12715

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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, 06:15
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, 06:50
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] 29 Aug 2017, 06:50
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