Which of the following is true about parallelogram?

Analyze the question: We need to pick the true property of a parallelogram's opposite angles.

Concept: A parallelogram is a quadrilateral with two pairs of parallel sides. Its key properties are:

• Opposite sides are equal and parallel.
• Opposite angles are equal.
• Adjacent angles are supplementary (add up to 180°).
• Diagonals bisect each other.

Step-by-step reasoning:

Let parallelogram ABCD have AB ∥ DC and AD ∥ BC.

1. Since AB ∥ DC, angles A and D are co-interior (allied) angles, so ∠A + ∠D = 180°.
2. Since AD ∥ BC, angles D and C are also co-interior, so ∠D + ∠C = 180°.
3. From steps 1 and 2: ∠A + ∠D = ∠D + ∠C, so ∠A = ∠C.
4. In the same way, ∠B = ∠D.

So opposite angles are equal.

Checking the options:

• A. Supplementary: This is true of adjacent angles, not opposite ones. (Opposite angles are supplementary only in the special case of a rectangle, where each is 90°.) Not generally true.
• B. Complementary: They would add up to 90°, which is impossible, since the four angles must total 360°.
• C. Equal: True, as shown above.
• D. Reflex: A reflex angle is greater than 180°. A parallelogram's angles are all less than 180°, so this is false.

Answer: C. opposite angles are equal

Exam tip: Remember "opposite = equal, adjacent = supplementary." Examiners often swap these two to trap you, so read the word opposite or adjacent carefully.