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Asked by Grace

Suppose the measures of the interior angles of a convex nonagon are nine numbers each separated by a value of 1 degree from its neighbors what is the measure of the second smallest angle?

The question tells us that the angles are nine consecutive numbers. If we call the smallest angle x, the nine angles are: x, x+1, x+2, x+3, x+4, x+5, x+6, x+7, and x+8. The sum of the interior angles of a convex polygon of n sides is: (n-2)*180. This makes the sum of the interior angles of a convex nonagon: 7*180=1260° This means if we add up our interior angles we get: x + x+1 + x+2+ x+3 + x+4 + x+5 +x+6 + x+7 + x+8 = 9x + 36 = 1260 If we solve for x: 9x + 36 = 1260 9x = 1224 x = 136 The second smallest angle is x+1 so 137° Hope that helps! ~ Sohini

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Sohini Khan
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