Work through the levels in order. Type your answer and press Check — open the worked solution if you get stuck. Answers like -6, 3/4 or 0.25 are typed exactly as shown.
Level 1 · Warm-up
1 A quadrilateral has angles of 90°, 90° and 100°. Find the fourth angle (in degrees).
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90 + 90 + 100 = 280, and 360 − 280 = 80°. Check: 90 + 90 + 100 + 80 = 360 ✓
2 What do the four angles of a quadrilateral add to (in degrees)?
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Two triangles at 180° each gives 360°.
3 A parallelogram has one angle of 65°. Find the angle NEXT to it (in degrees).
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180 − 65 = 115° (neighbouring angles of a parallelogram add to 180°).
Level 2 · Core
4 A quadrilateral has angles of 120°, 75° and 60°. Find the fourth angle (in degrees).
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120 + 75 + 60 = 255, and 360 − 255 = 105°. Check: 120 + 75 + 60 + 105 = 360 ✓
5 A rhombus has one angle of 50°. Find the angle next to it (in degrees).
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A rhombus is a parallelogram, so neighbouring angles add to 180: 180 − 50 = 130°.
6 A quadrilateral has angles of 85°, 95° and 70°. Find the fourth angle (in degrees).
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85 + 95 + 70 = 250, and 360 − 250 = 110°. Check: 85 + 95 + 70 + 110 = 360 ✓
Level 3 · Challenge
7 A quadrilateral has both pairs of opposite sides parallel and one angle of 90°. Name the shape.
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Two pairs of parallel sides make it a parallelogram, and its neighbours are 180 − 90 = 90°, so every angle is 90°. It is a rectangle.
8 In a parallelogram, one angle is 3 times as big as the angle next to it. Find the SMALLER of the two angles (in degrees).
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x + 3x = 180, so 4x = 180 and x = 45°. The four angles are 45, 135, 45 and 135, totalling 360 ✓
9 A quadrilateral has angles x, x, x and 120°. Find x (in degrees).
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360 − 120 = 240 is shared by three equal angles, so x = 80°. Check: 80 + 80 + 80 + 120 = 360 ✓