Geometry Practice Test 3

Internal angles of the first regular polygon = 2x
Internal angles of the second regular polygon = 3x
2x + E = 180
E = 180 - 2x, where E is the external angle of regular polygon
Similarly, E = 180 - 3x
Number of sides of the 1st polygon =

360

180−2x

Number of sides of the other polygon =

360

180−3x

Ratio of the number of sides = 1 : 2

360 180−2x

360 180−3x

=

1

2

360

180−2x

×

180−2x

360

=

1

2

360 − 6x = 180 − 2x
x =

180

4

x = 45
Now number of sides of the first polygon
=

360

180−90

=

360

90

= 4
Other sides =

360

180−145

=

360]

45

= 8
Number of sides = 4, 8