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. A ⭐ Bonus Challenge at the end is extra credit — skip it if the rest was hard work.
Level 1 · Warm-up
1 What do the three angles of a triangle add to?
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180°.
2 An isosceles triangle has an apex of 40°. Write the total of the two base angles and the size of each.
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140° between them, so 70° each.
3 How many faces does a hexagonal pyramid have?
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7.
Level 2 · Core
4 Three angles meet at a point: 135°, 90° and one more. How big is the third?
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360 − 135 − 90 = 135°.
5 Write the number of faces, edges and vertices of a hexagonal pyramid.
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7 faces, 12 edges and 7 vertices.
6 A quadrilateral has angles of 120°, 80° and 100°. How many degrees is the fourth?
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60°.
Level 3 · Challenge
7 An isosceles triangle has an apex of 40°, and one base angle is extended along a straight line.1 Each base angle is 70°.
2 The angle outside the triangle is 110°.
3 The angle outside the triangle is 140°.
Which statements are correct?
2 The angle outside the triangle is 110°.
3 The angle outside the triangle is 140°.
Which statements are correct?
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(180 − 40) ÷ 2 = 70° (1 ✓), and 180 − 70 = 110° (2 ✓, 3 ✗). 1 and 2.
8 Write the number of edges of a hexagonal prism, and the number of its vertices.
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18 edges and 12 vertices.
9 For a hexagonal pyramid, what do the faces, edges and vertices add to altogether?
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26.