Maths......what to do???????????

Question

http://i385.photobucket.com/albums/oo299/Morshidul/Image296.jpg

This given design is made up of 6 congruent parallelograms. what is the measure of angle "1"

Answer 1

Angle 1 is 120° or ⅔ π radians.

For the six parallelograms to be congruent, each of the six acute angles whose vertex is at the centre of the six-sided star must be equal: that is, 60°, as their total must be 360°.

Now, let angle 2 be the acute angle which is interior to the same parallelogram as is angle 1 and which is one of the six angles above-mentioned at the centre of the star.

Then, the obtuse angle 1 must be 120°: forasmuch as angles 1 and 2 are interior angles on the same side of a transversal betwixt parallel lines and, therefore, supplementary to each other.

I hope that this will be of assistance to you.