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.
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kevincanspain
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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...
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...
