"The central angles of a circle are six consecutive odd integers. What is the measure of the largest prime angle?" Please answer the question, thank you!

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- Feb 16th 2013, 04:26 PMevilgummybearAnother circle problem.
"The central angles of a circle are six consecutive odd integers. What is the measure of the largest prime angle?" Please answer the question, thank you!

- Feb 16th 2013, 06:56 PMzhandeleRe: Another circle problem.
I'm not entirely sure I understand the problem. I think you want five angles measured in degrees that add up to 360. If so, the five numbers are easy enough to find by trial and error. They are 69, 71, 72, 73, and 75. Now you just have to figure out which of these numbers is prime. 75 is not a prime number, but I think 73 is.

- Feb 16th 2013, 07:16 PMSorobanRe: Another circle problem.
Hello, evilgummybear!

Quote:

The central angles of a circle are six consecutive odd integers.

What is the measure of the largest prime angle?

Consecutive odd integers differ by 2.

The six angles are: .$\displaystyle x,\,x+2,\,x+4,\,x+6,\,x+8,\,x+10$

Their sum is 360^{o}: .$\displaystyle 6x + 30 \:=\:360 \quad\Rightarrow\quad x \:=\:55$

The six angles are: .$\displaystyle 55^o,\,57^o,\,59^o,\,61^o,\,63^o,\,65^o$

The largest prime angle is $\displaystyle 61^o.$