2005 iTest Problems/Problem 22

Problem

A regular $n$ -gon has $135$ diagonals. What is the measure of its exterior angle, in degrees? (An exterior angle is the supplement of an interior angle.)

Solution 1

The formula for the number of diagonals of an $n$ -gon is $\frac{n(n-3)}{2}$ . Setting this expression equal to $135$ , we find that $n=18$ , as $n$ must be positive. The exterior angle of a regular polygon with $n$ sides in degrees is $\frac{360}{n}$ . Plugging in $n=18$ , our desired answer is $\frac{360}{18}=\boxed{20^\circ}$

2005 iTest (Problems, Answer Key)
Preceded by: Problem 21	Followed by: Problem 23
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 • 41 • 42 • 43 • 44 • 45 • 46 • 47 • 48 • 49 • 50 • 51 • 52 • 53 • 54 • 55 • 56 • 57 • 58 • 59 • 60 • TB1 • TB2 • TB3 • TB4

Page

Toolbox

Search

2005 iTest Problems/Problem 22

Problem

Solution 1

See Also