JAMB - Mathematics (1987 - No. 44)

Three angles of a nonagon are equal and the sum of six other angles is 1110o. Calculate the size of one of the equal angles.
210o
150o
105o
50o

Explanation

Sum of interior angles of any polygon is (2n - 4) right angle; n angles of the nonagon = 9

where 3 are equal and 6 other angles = 1110o

( 2 x 9 - 4)90o = (18 - 4)90o

= 14 x 90o = 1260o

9 angles = 12600, 6 angles = 1110o

Remaining 3 angles = 1260o - 1110o = 150o

size of one of the3 angles \(\frac{150}{3}\) = 50o

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