Question

A diagram shows a regular octagon and an equilateral triangle joined together(the diagram is in the image). How many sides does this polygon have?

Answer 1

Answer:

maybe 11 is the answer because triangle is also their

Answer 2

Answer:

The number of sides is 24.

Step-by-step explanation:

Let the unknown polygon be x.
Angle ABC is the interior angle of x.
Therefore, let Angle ABC = iₓ

iₓ = 360° - (interior angle of octagon + interior angle of equilateral triangle)  [angles around a point = 360°]

Interior angle of octagon = 180° - ($\frac{360}{8}$)
                                          = 180° - 45° (is the exterior angle of the octagon)
Interior angel of octagon = 135°

iₓ = 360° - (135° + 60°)  [in equilateral triangle, all interior angles are 60°]
iₓ = 360° - 195°
iₓ = 165°

Therefore, interior angle of the unknown polygon is 165°.
Now, to find the number of sides (N):

N = 360/exterior angle

exterior angle = 180° - 165° = 15°

N = 360°/15°
N = 24

Therefore, number of sides of the unknown polygon is 24 (icositetragon or icosikaitetragon)

Hope it helps; feel free to ask questions if not clear.