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 triangle has angles of 50° and 60°. Find the third angle (in degrees).
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50 + 60 = 110, and 180 − 110 = 70°. Check: 50 + 60 + 70 = 180 ✓
2 A triangle has angles of 90° and 20°. Find the third angle (in degrees).
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180 − 90 − 20 = 70°, or use the shortcut 90 − 20 = 70.
3 What is each angle of an equilateral triangle (in degrees)?
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180 ÷ 3 = 60°.
Level 2 · Core
4 A triangle has angles of 105° and 32°. Find the third angle (in degrees).
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105 + 32 = 137, and 180 − 137 = 43°. Check: 105 + 32 + 43 = 180 ✓
5 An isosceles triangle has an apex angle of 80°. Find each base angle (in degrees).
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180 − 80 = 100, and 100 ÷ 2 = 50°. Check: 80 + 50 + 50 = 180 ✓
6 An isosceles triangle has base angles of 65° each. Find the apex angle (in degrees).
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65 + 65 = 130, and 180 − 130 = 50°. Check: 65 + 65 + 50 = 180 ✓
Level 3 · Challenge
7 A right-angled triangle has one angle of 28°. Find its third angle (in degrees).
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The two non-right angles share 90°, so the third is 90 − 28 = 62°. Check: 90 + 28 + 62 = 180 ✓
8 Do the angles 85°, 55° and 30° make a triangle? Answer yes or no.
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85 + 55 + 30 = 170, which is not 180, so the answer is no — no such triangle exists.
9 An isosceles triangle has one angle of 96°. Find the other two angles (in degrees, separated by a comma).
Show worked solution
Two 96° angles would already be 192°, more than 180, so the 96° must be the apex. The base angles are (180 − 96) ÷ 2 = 42° and 42°. Check: 96 + 42 + 42 = 180 ✓