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 30° and 60°. Find the third angle, in degrees.
Show worked solution
180 − 30 − 60 = 90°. It is a right-angled triangle.
2 How many equal sides does a scalene triangle have?
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None. All three sides are different lengths.
3 What is each angle of an equilateral triangle, in degrees?
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180 ÷ 3 = 60°.
Level 2 · Core
4 An isosceles triangle has base angles of 40°. Find the apex angle, in degrees.
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180 − 40 − 40 = 100°.
5 An isosceles triangle has an apex angle of 90°. Find each base angle, in degrees.
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2x = 90, so x = 45°. This is a right-angled isosceles triangle.
6 A triangle has interior angles 55° and 65°. Find the exterior angle opposite them, in degrees.
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55 + 65 = 120°.
Level 3 · Challenge
7 Can a triangle have angles 70°, 70° and 50°? If yes, name it by sides.
Show worked solution
They add to 180 ✓, and two equal angles mean two equal sides → isosceles.
8 A triangle has angles x, 2x and 3x. Find x, in degrees.
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x + 2x + 3x = 180 → 6x = 180 → x = 30°. The angles are 30, 60 and 90.
9 An isosceles triangle has one angle of 100°. Find the other two, in degrees. (list them separated by commas)
Show worked solution
The 100° must be the apex, since two 100° angles would exceed 180. So the base angles are (180 − 100) ÷ 2 = 40° and 40°.