Brainsteem Mathematics Challenges: Angles in a Pentagon
Question
The interior angles of a pentagon are chosen in such a way that they form a sequence of consecutive even numbers.
What is the size of the largest angle?
This is from the recent UKMT JMO, so for lower secondary students.
A reminder that these questions should be done without any electronic aid; in this case, one shouldn't really be needed anyway!
The first correct answer and further interesting comments will be rewarded with an upvote. Please show your method, or at least the key steps.
Enjoy!
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@rycharde manages the AAKOM project and the MAP Trail.
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The largest angle is 112 degrees.
The first step is knowing that the sum of the interior angles of a n-sided polygon adds up to 180(n-2) degrees.
For a pentagon, that is 540 degrees, with an average interior angle of 108 degrees. Since we want a sequence of consecutive even numbers, that sequence is 104, 106, 108, 110, 112.
:-)
Have just posted this extension: Brainsteem Mathematics Challenges: Even Angles in a Polygon.
Agreed that 112 degrees is the largest interior angle of the said pentagon.
This sounds interesting @rycharde!
Thanks, have you tried the extension?
I'm not turning off my a/c for any post, not in this heat.
You got me there! My aircon is on most of the time, although these few days am up in the mountains and is much cooler than the big smog. It's still tropical, but the monsoon season is a relief.