Is the question right

Geometry Level 1

Does there exists a triangle with each angle of the triangle is an integer multiples of 17

Yes No Insufficient Information

Department 8 by Department 8 , 27, Israel

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2 solutions

Rishabh Jain
Feb 1, 2016

Let the angles of the triangle be 17 m , 17 n a n d 17 p \color{darkviolet}{17m},\color{#D61F06}{17n} ~and~\color{#EC7300}{17p} (for some integers m,n,p)

Then by Angle Sum Property: 17 m + 17 n + 17 p = 180 ° \color{darkviolet}{17m}+\color{#D61F06}{17n} +\color{#EC7300}{17p}=180° ⇒ m + n + p = 180 17 \Rightarrow \color{darkviolet}{m}+\color{#D61F06}{n} +\color{#EC7300}{p}=\dfrac{180}{17} which is absurd since the sum of integers(m,n,p) cannot turn to a fraction!!

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So fast!! !!!!!

Department 8 - 5 years, 4 months ago

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Yup.. I love being fast(joking...:P)....BTW you should correct the grammar of the question...

Rishabh Jain - 5 years, 4 months ago

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Sorry made it pretty fast check it now.

Department 8 - 5 years, 4 months ago

17 17 is a prime number.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

If I change the question to integral multiples of 16, what would your answer be, because in this case the number is not prime.

Kushagra Sahni - 5 years, 4 months ago

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Exactly.... Prime has nothing to do in this question.....

Rishabh Jain - 5 years, 4 months ago

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What's more relevant is if the number in the original problem (17 in this case) divides into 180 degrees. If it can, then such a triangle can exist.

Oli Hohman - 5 years, 4 months ago

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