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

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Bunuel
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A non-symmetrical arrow point exists such that the angle of the back [#permalink] New post   28 Aug 2017, 23:38
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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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AbhijitGoswami
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Re: A non-symmetrical arrow point exists such that the angle of the back [#permalink] 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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chaitanya1317
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Re: A non-symmetrical arrow point exists such that the angle of the back [#permalink] New post   29 Aug 2017, 07:50
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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] New post   17 Dec 2017, 06:14
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Bunuel is there an easier way to answer this question ?
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Re: A non-symmetrical arrow point exists such that the angle of the back [#permalink] New post   12 Dec 2023, 11:29
I solved this using a different approach which took me about 10-15seconds.
Do correct me if I'm wrong.

The angle behind the 105deg angle would be 255degrees (360-105)
Then we just take the sum of interior angles of the quadrilateral = 360
==> a+b+c+255 = 360
==> a+b+b = 105 degrees (Option A)
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Re: A non-symmetrical arrow point exists such that the angle of the back [#permalink]
12 Dec 2023, 11:29
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