complementary angles are two angles whose total degrees adds up to 90o supplementary angles are two angles whose total degrees adds up to 180o
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In a right angled triangle, the two non-right angles are complementary, because in a triangle the three angles add to 180°, and 90° has already been taken by the right angle. When two angles add to 90°, we say they "Complement" each other.
Well it could be complementary or supplementary because they don't have to share a vertex yet I think you mean something like the vertical angle. You can go research vertical angles. I'll give you a link for the vertical angles. http://www.mathsisfun.com/geometry/vertical-angles.html
A diagonal has no shape, it is a straight line between the angles of a multi-sided figure.
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mathematics is a subject, it is?