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# Interior Angle Problem | AIME I, 1990 | Question 3

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1990 based on Interior Angle.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1990 based on Interior Angle.

## Interior Angle Problem – AIME I, 1990

Let $P_1$ be a regular r gon and $P_2$ be a regular s gon $(r \geq s \geq 3)$ such that each interior angle of $P_1$ is $\frac{59}{58}$ as large as each interior angle of $P_2$, find the largest possible value of s.

• is 107
• is 117
• is 840
• cannot be determined from the given information

### Key Concepts

Integers

Polygons

Algebra

AIME I, 1990, Question 3

Elementary Algebra by Hall and Knight

## Try with Hints

Interior angle of a regular sided polygon=$\frac{(n-2)180}{n}$

or, $\frac{\frac{(r-2)180}{r}}{\frac{(s-2)180}{s}}=\frac{59}{58}$

or, $\frac{58(r-2)}{r}=\frac{59(s-2)}{s}$

or, 58rs-58(2s)=59rs-59(2r)

or, 118r-116s=rs

or, r=$\frac{116s}{118-s}$

for 118-s>0, s<118

or, s=117

or, r=(116)(117)

or, s=117.