Video: AQA GCSE Mathematics Higher Tier Pack 2 • Paper 3 • Question 2

Given that the interior angles of a quadrilateral are 75°, 65°, 120°, and 100°. What kind of quadrilateral could it be? Circle your answer. [A] parallelogram [B] Rectangle [C] Kite [D] Trapezium

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Video Transcript

Given that the interior angles of a quadrilateral are 75 degrees, 65 degrees, 120 degrees, and 100 degrees. What kind of quadrilateral could it be? Circle your answer. Is it a parallelogram, a rectangle, a kite, or a trapezium?

Let’s begin by thinking about what we know about each of these quadrilaterals and their properties. A parallelogram has two pairs of equal and parallel sides. The opposite angles in a parallelogram are also equal.

You could say that a rectangle is a special type of parallelogram. It also has two pairs of equal and parallel sides. This time though, its angles are all 90 degrees.

A kite has two pairs of equal sides, though they’re not parallel. It also has one pair of equal angles. A trapezium has a pair of parallel sides but no equal sides, nor equal angles. The only type of trapezium that does have equal sides and equal angles is called an isosceles trapezium.

Notice how each of the interior angles of the quadrilateral in our question are different. It therefore cannot be a parallelogram, nor can it be a rectangle, nor can it be a kite. In this case then, our quadrilateral could be a trapezium.

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