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Quadrilateral Angle Properties
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Quadrilateral Angle Properties
Use angle facts to solve the design challenges. Show your working for calculations. Angles are measured in degrees (°).
Angle facts in a design studio
A design team is planning a tiled courtyard. Each tile is a quadrilateral, and the team needs to check that its angles fit together correctly.
1.The team divides a quadrilateral tile into two triangles by drawing one diagonal. Each triangle has an angle sum of 180°. What is the total interior angle sum of the quadrilateral?
- 180°
- 270°
- 360°
- 540°
2.A rectangular tile has four equal interior angles. What is the size of each angle?
3.A parallelogram tile has one angle of 68°. Opposite angles are equal, and neighbouring angles add to 180°. Find all four interior angles.
4.A quadrilateral tile has angles 85°, 95° and 85°. Calculate its fourth angle.
5.A kite-shaped tile has angles 74°, 74°, 132° and x°. Find x.
6.A quadrilateral has angles x°, 2x°, 3x° and 4x°. Find x, then state all four angles.
7.A trapezium has one pair of parallel sides. The two interior angles along its left side are 110° and 70°. What is the sum of the two angles along its right side?
8.A parallelogram designer claims, “If one angle is 90°, all four angles must be 90°.” Is the claim true or false? Explain using the angle properties of a parallelogram.
9.A quadrilateral’s angles are (2y + 10)°, (3y − 20)°, (y + 30)° and (4y − 20)°. Find y and the four angle sizes.
10.Explain why drawing a diagonal through any quadrilateral proves that its interior angles sum to 360°.
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