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This problem trains for: SAT-I, GMAT, AMC-10, AMC-8.

A convex quadrilateral has two supplementary angles. Which one of the following statements could be true?

Remember that supplementary angles are angles that add up to 180°.

The problem does not specify if the supplementary angles are opposite or adjacent, or any of the two.

Therefore, a parallelogram satisfies since it has two adjacent angles that add up to 180°:

figure

A kite is a parallelogram, therefore it also satisfies.

A quadrilateral that has two opposite angles that add up to 180° can be inscribed in a circle (it is a cyclic quadrilateral.)

figure

The two opposite angles of a cyclic (inscribable) quadrilateral add up to 180° because the inscribed angles they subtend add up to a complete circle: 360°.