A polygon has n sides. Three of its exterior angels are 70 degrees, 80 degrees and 90 degrees. The remaining #(n-3)# exterior angels are each 15 degrees. How many sides does this polygon have?

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Answer 1 · 2018-03-08T13:23:03

Polygon has #11# sides

Sum of the exterior angles of any polygon is always #360^@#.

As three angles are #70^@,80^@# and #90^@# and remaining #n-3# angles are #15^@# and their sum is #360^@#, we have

#70+80+90+15(n-3)=360#

or #15(n-3)=360-70-80-90=120#

and #n-3=120/15=8#

i.e. #n=11#

Hence, polygon has #11# sides