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The measures of the interior angles of a convex decagon are 21x°, 154°, 118°, 106°, 15x°, 165°, 172°, 162°, 151°, and 160°. What is the measure of the smallest interior angle?

 Apr 2, 2021
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ANSWER: $\boxed{105^\circ}$

 

SOLUTION: The sum of the angles of a convex polygon with $n$ sides will be $180*(n-2)$. For a decagon, the sum of the sides is $180*8=1440$. That means $160+151+162+172+165+15x+106+118+154+21x=1440$.

 

Moving constants to the right side and grouping gives $x=7$

 

That means the $21x$ angle is equal to $21*7=147$, and the $15x$ angle is equal to $15*7=105$. Comparing, you see that $105$ is the smllest angle, so your answer is $\boxed{105^\circ}$

 Apr 2, 2021

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