Question

If three angles of a quadrilateral are equal, then the quadrilateral is ______.

Options

• rectangle

• rhombus

• not a parallelogram

• parallelogram

Answer 1

If three angles of a quadrilateral are equal, then the quadrilateral is not a parallelogram.

Explanation:

If three angles of a quadrilateral are equal, say ∠A = ∠B = ∠C = x, the sum of the interior angles equals 3x + y = 360°. In a parallelogram, opposite angles must be equal, which would require the fourth angle to also equal x. Unless x = 90° (where all four angles equal 90° to form a rectangle), the opposite angles do not match, meaning the general quadrilateral is not a parallelogram.