The value of w to the nearest whole number is 16°
A polygon is called regular if it has equal sides and angles. Thus, a regular triangle is an equilateral triangle, and a regular quadrilateral is a square.
Decagon has 10 sides.
sum of interior angles of a polygon = ( n - 2) x 180
where n = number of sides of polygon
here n = 10
sum of interior angle = ( 10 - 2) x 180 which is 1440°
If a regular polygon has equal angles and each angle is (8w + 17)
then 10( 8w + 17) = 1440
divide both sides by 10
8w + 17 = 144
8w = 144 - 17
8w = 127
w = 127/8
w = 15.875
to the nearest degree, W = 16°
In conclusion w = 16° to the nearest degree.
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