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 angles of any triangle add to?
Show worked solution
180°.
2 Fill in the two totals: the angles of a triangle add to ?, and the angles of a quadrilateral add to ?.
Show worked solution
180° and 360°.
3 An equilateral triangle has three equal angles. How many degrees is each one?
Show worked solution
60°.
Level 2 · Core
4 An isosceles triangle has an apex angle of 100°. How big is each base angle?
Show worked solution
40° each.
5 An isosceles triangle has base angles of 65°. Give the total of the two base angles and the size of the apex angle.
Show worked solution
130°, so the apex is 180 − 130 = 50°.
6 A roof truss is an isosceles triangle with an apex angle of 30°. How many degrees is each base angle?
Show worked solution
75°.
Level 3 · Challenge
7 A kite has 100° at the top and 60° at the bottom; the other two angles are equal.1 The four angles add to 360°.
2 x = 100°.
3 x = 80°.
Which statements are correct?
2 x = 100°.
3 x = 80°.
Which statements are correct?
Show worked solution
Quadrilateral, so 360° (1 ✓). (360 − 160) ÷ 2 = 100° (2 ✓, 3 ✗). 1 and 2.
8 A kite has 120° at the top and 60° at the bottom. Give the total of the two equal angles, and the size of each.
Show worked solution
360 − 180 = 180°, so each is 90°. Check: 120 + 90 + 60 + 90 = 360.
9 A triangle has one line of symmetry. Two of its angles are 50° and 80°. How many degrees is the third angle?
Show worked solution
50° — which matches the other 50°, as the fold requires.