# trig

the angle in one regular polygon is to that in another as 3:2 and the number of the sides in first is twice that in second determine the the number of sides of 2 polygons

1. 👍 0
2. 👎 0
3. 👁 192
1. let the number of sides of the second be n
then the number of sides of the first is 2n

size of angle of the second = 180(n-2)/n
size of angle of the first = 180(2n-2)/(2n)

but that ratio is 3:2

[180(n-2)/n] / [180(2n-2)/(2n)] = 2/3
after some canceling and cross-multiplying ...
n = 4

one polygon is a square , the other is an octogon

check:
(4 sides and 8 sides)
each angle in a square is 90°, each angle in an octogon is 135°
135 : 90 = 3 : 2

1. 👍 0
2. 👎 0

## Similar Questions

1. ### Geometry

The sum of the interior angles of polygon is 1800. Find the number of sides in the polygon and, what do you call that polygon?

asked by Anal-G on January 20, 2011
2. ### maths

each interior angle of a regular polygon is 18 degree more than eight times an exterior angle. the number os sides of polygon is.

asked by polygon on March 28, 2012

asked by BaileyBubble on December 12, 2012
4. ### geometry

if each angle in a regular polygon is 157.5 degrees, how many sides does the polygon have?

asked by Anonymous on September 23, 2009
1. ### Maths urgent

One regular polygon has twice as many sides as another. If the ratio of the interior angles of the first to that of second is 5:4, find the number of sides in each polygon?

asked by Rabinprakash Dahal on September 13, 2015
2. ### maths

The diagram shows part of a regular polygon. work out how many sides the polygon has. (it is 156 degrees).

asked by corinna on October 29, 2007
3. ### Math_ Geometry

The sum of the interior angles of a regular polygon equals 1260 degrees. How many sides does a polygon have?

asked by Sarah on July 27, 2017
4. ### Geometry

1 - Complete this statement: A polygon with all sides the same length is said to be___. a. regular b. equilateral *** c. equiangular d. convex 2- A road sign is in the shape of a regular heptagon. What is the measure of each angle

asked by Anonymous on January 13, 2019
1. ### geometry

The Polygon Angle-Sum Theorem states the following: The sum of the measures of the angles of an n-gon is ____. (1 point) (n – 1)180o (n – 2)180o 9. What is the measure of one angle in a regular 16-gon? (1 point) 2,520o 202.5o

asked by josh on December 31, 2012
2. ### math

The measure of an interior angle of a regular polygon is 135 degrees. Find the number of sides in the polygon. This is what I tried: 180(x-2)=135 [Interior Angle Sum Theorem] x-2=.75 x=2.75 That can't be right though. Help? Not

asked by Emily on March 27, 2007
3. ### math214

A student asks whether a polygon whose sides are congruent is necessarily a regular polygon and whether a polygon with all angles congruent is necessarily a regular polygon. How do you answer?

asked by alicia on February 16, 2010
4. ### Cycle geometry

An interior angle of a regular convex polygon is 162(degrees). Find the number of sides.

asked by Christopher on June 29, 2015