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.
15 questions · official format, shuffled order
1 Three angles meet on a straight line. One is 48° and another is twice that. What is the third angle?
Show worked solution
180 − 48 − 96 = 36°.
2 Four angles meet at a point. What is the missing angle?
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110 + 85 + 75 = 270, and 360 − 270 = 90°.
3 Two straight lines cross. One of the four angles is 37°. What do the other three angles add up to?
Show worked solution
The four angles total 360°, so the other three total 360 − 37 = 323° (they are 143°, 37° and 143°).
4 This isosceles triangle has a base angle of 72°. What is the angle at the top?
Show worked solution
180 − 72 − 72 = 36°.
5 What is the reflex angle between the hands of this clock?
Show worked solution
From 12 to 8 clockwise is 8 × 30 = 240° — the reflex angle. The short way round is 120°.
6 An angle measures 127°.1 It is an obtuse angle.
2 The reflex angle on the other side of it measures 233°.
3 The angle next to it on the straight line measures 63°.
Which statements are correct?
2 The reflex angle on the other side of it measures 233°.
3 The angle next to it on the straight line measures 63°.
Which statements are correct?
Show worked solution
127° is between 90° and 180°, so obtuse (1 ✓). 360 − 127 = 233° (2 ✓). 180 − 127 = 53°, not 63° (3 ✗). 1 and 2.
7 This kite has a line of symmetry down the middle. Its top angle is 116° and its bottom angle is 54°. What is each side angle?
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360 − 116 − 54 = 190 for the two side angles together, so each is 190 ÷ 2 = 95°.
8 Two angles of a triangle are 48° and 67°. One side of the triangle is extended at the third corner. How big is the angle outside the triangle at that corner?
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Inside: 180 − 48 − 67 = 65°. Outside, on the straight line: 180 − 65 = 115°.
9 A round pizza is cut into 8 equal slices and 3 are eaten. What is the angle at the centre of the piece that is left?
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360 ÷ 8 = 45° a slice. 5 × 45 = 225°.
10 Kai faces north. He turns 225° clockwise, then 90° anticlockwise. Which direction is he facing now?
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225° clockwise from north is south-west. 90° anticlockwise from south-west is 135° clockwise from north: south-east.
11 Two straight lines cross. One of the angles is 124°. What is the difference between the largest and smallest angles formed?
Show worked solution
The small angles are 180 − 124 = 56°. 124 − 56 = 68°.
12 Three angles sit on a straight line: 35°, an unknown angle, and a right angle.1 The unknown angle is 55°.
2 The two smaller angles add to a right angle.
3 The unknown angle is obtuse.
Which statements are correct?
2 The two smaller angles add to a right angle.
3 The unknown angle is obtuse.
Which statements are correct?
Show worked solution
180 − 90 − 35 = 55° (1 ✓). 35 + 55 = 90, a right angle (2 ✓). 55° is acute, not obtuse (3 ✗). 1 and 2.
13 What is the smaller angle between the hands of this clock?
Show worked solution
The minute hand is at 180°. The hour hand is halfway from 4 to 5: 4.5 × 30 = 135°. The difference is 45°.
14 An equilateral triangle is drawn on top of a square, sharing one side. At one shared corner, what is the reflex angle on the outside of both shapes?
Show worked solution
360 − 90 − 60 = 210°.
15 Five angles meet at a point. Four of them are 72°, 58°, 90° and 65°. What is the fifth?
Show worked solution
72 + 58 + 90 + 65 = 285. 360 − 285 = 75°.