are the opposite angles of a kite always, sometimes, or never supplementary

Question

anonymous · Answer

please help

mathstudent55 · Answer

I think I figured it out.

mathstudent55 · Answer

Here's a kite.
The upper two sides are congruent, and the lower two sides are congruent, but all 4 sides are not congruent.
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mathstudent55 · Answer

A kite has 4 interior angles. The two labeled x are congruent to each other. The other two angles are not congruent.
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mathstudent55 · Answer

The sum of the  the measures of the interior angles of a kite is 180(n - 2), for n = 4, so it is 180 * 2 = 360.

mathstudent55 · Answer

The sum of the measures of the angles, then is x + x + y + z = 360, or
2x + y + z = 360

mathstudent55 · Answer

If the angles y and z were supplementary, then y + z = 180, so you get
2x + 180 = 360
2x = 180
x = 90

mathstudent55 · Answer

Here is a case where the angles labeled x are both 90 degrees, and the angles labeled y andf z are supplementary.
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mathstudent55 · Answer

The answer is "sometimes."