25 the completed construction of a regular hexagon is shown below. explain why △acf is a 30º-60º-90º triangle. here is what i have so far, can anyone me finish this proof out? ! 1) based on the theorem of a 30°-60°-90° triangle the sides are in the ratio 1 : 2 : √3 1 → short leg 2 → hypotenuse √3 → long leg since this is a regular hexagon that means that each side is the same length. a normal hexagon equivalent and has six angles of 120° .angle f must then equal 60 degrees because it is half of the angle of the regular hexagon.

You can prove that angle C is 30°. This is because we know that angle B is 120° also, and cointerior angles add to 180°, which makes angle BCF 60°. Then we can divide this by 2 as angle BCF is bisected by AC, so therefore angle ACF is 30° as 60 ÷ 2 = 30.

You can then prove angle A is 90°. First we can find angle BAC because it is part of a triangle, and angles in a triangle add to 180°. This means we can do 30 + 120 = 150, and 180 - 150 = 30° which is angle BAC. Then we do 120 - 30 = 90, as the whole of angle BAF is 120°.

I hope this helps!