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Describes a pair of adjacent angles whose noncommon sides are opposite rays?
a linear pair!
Are two adjacent angles whose exterior sides are opposite rays always complementary?
No? Wouldn't they then be supplementary? Opposite rays make a straight angle/line, and if the exterior sides made the straight angle, the adjacent angles would be supplementary. ...Right?
Why is the square is a special rectangle?
A square is a rectangle whose adjacent sides are equal.
What do you do in trigonometry when you are only given the opposite and adjacent sides?
That depends what you're asked for. If you're asked for the tangent of the angle, divide (opposite)/(adjacent) . If you're asked for the hypotenuse of the triangle, it's sqrt( opposite2 + adjacent2 ) . If you're asked for the cosine of the angle, it's (adjacent)/(hypotenuse) . If you're asked for the other acute angle, it's the angle whose tangent is (adjacent)/(opposite) . If you're not asked for anything, then get your jacket, chew some gum, and go home.
Why are squares classified as rectangles?
By definition a rectangle is a four-sided figure whose opposite sides are equal in length and corners are right angles. The definition doesn't say anything about the lengths of adjacent sides, though. A square has the same definition as a rectangle with the added criterion that adjacent sides are also equal in length. That means a square is a more-specific type of rectangle.
