💯 Maths

# 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?

1 answers

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