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# 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?

Mar 8, 2018

Polygon has $11$ sides

#### Explanation:

Sum of the exterior angles of any polygon is always ${360}^{\circ}$.

As three angles are ${70}^{\circ} , {80}^{\circ}$ and ${90}^{\circ}$ and remaining $n - 3$ angles are ${15}^{\circ}$ and their sum is ${360}^{\circ}$, we have

$70 + 80 + 90 + 15 \left(n - 3\right) = 360$

or $15 \left(n - 3\right) = 360 - 70 - 80 - 90 = 120$

and $n - 3 = \frac{120}{15} = 8$

i.e. $n = 11$

Hence, polygon has $11$ sides