Question

a design is made up of 8 congruent. isosceles trapezoids: this design makes up an octagon in the inside shape as well as outside.

what is the measure in degrees of angle y?
(angle y is inside one of th trapezoids)

so far i caculated 180(8-2)/8 so i got 135 degress but the answer is 112.5 its given.. so im stuck with the 135 degrees since i think i have to do another step with it..

Answer 1

its page 54

Answer 2

If you draw radial lines from the centre of the 2 concentric octagons to the vertices of the inner octagon 8 isoceles triangles are formed with all of them sharing one vertex in common which is the centre of the octagon.The angle at this vertex for each of these triangles is
360/8 = 45.If this angle is 45 degrees and the triangle is isoceles (because the radial distance from the centre to any vertex is the same and the triangle is formed by two such radial lines) then the other two angles of this triangle are
(180-45)/2 = 67.5. This angle is a supplementary angle to the angle y.Hence y is,
180-67.5=112.5 degrees.