The formula of the measurement of an exterior angle of a regular polygon is
β = 360°/n
where β = exterior angle and n = number of sides
Therefore,
n = 360°/β = 360°/18° = 20 sides
7x - 8 = 8 + 3x
7x - 3x = 8 + 8
4x = 16
x = 16/4
x = 4
The length of OM is 4/3 the length of OJ, and the length of ON is 4/3 the length of OK. Thus, two pairs of sides from the triangles are proportional to each other.
Also, angle O from one of the triangles is equal to angle O of the other triangle because they are the same angle.
Thus, the two triangles are similar by SAS (side-angle-side) similarity theorem. This theorem is quite similar to the SAS congruence theorem.
To make a similarity statement, we just have to match corresponding parts when naming the triangle.
Similarity statement: ΔOJK~ΔOMN
