Polygon

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kevincanspain: GMAT Instructor; Posts: 613; Joined: Thu Mar 22, 2007 6:17 amFollowed by: 64 members; Location: madrid; Thanked: 171 times; GMAT Score:790

by kevincanspain » Sun Aug 26, 2007 2:44 am

R is a convex polygon. Does R have at least 8 sides?

(1) Exactly 3 of the interior angles of R are greater than 80 degrees.
(2) None of the interior angles of R are less than 60 degrees.

Kevin Armstrong
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Source: Beat The GMAT — Data Sufficiency | Sun Aug 26, 2007 2:44 am

beny: Master | Next Rank: 500 Posts; Posts: 214; Joined: Fri Jul 20, 2007 1:35 am; Thanked: 3 times

by beny » Sun Aug 26, 2007 6:21 am

I think the answer is A

1. Exactly 3 angles are greater than 80. Assume these angles are the maximum value of 179. 3*179 = 537.

The total interior angles of an octogon is 1080. 1080-537=543.

This means that the remaining 5 angles must sum to 543.

543/5=~109.

Therefore, it is impossible to be an octogon w/o at least one of the remaining 5 angles exceeding 80 degrees.

2. Tells you nothing... all the angles in a regular convex polygon that are quadrilateral and higher have interior angles of 90 or greater anyway...

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