Year 5 angles and polygons worksheet answers to download as PDF

These Year 5 angles and polygons worksheet answers give a full worked solution to all 21 questions of the angles and polygons worksheet. Try each question yourself first, then check your method step by step.

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Answer to Question 1
1. 30° is acute (less than 90°).
2. 90° is a right angle (exactly one quarter turn).
3. 135° is obtuse (between 90° and 180°).
4. 200° is reflex (between 180° and 360°).
5. 180° is a straight angle (exactly a half turn).
6. 350° is reflex (between 180° and 360°).
Answer to Question 2
1. A is acute, B is obtuse, C is reflex.
2. A is less than a right angle, about 40°. B is a bit more than a right angle, about 120°. C is more than a straight line, about 250°.
3. A (40°), B (120°), C (250°).
Answer to Question 3
1. x = 180 − 130 = 50°.
2. x = 180 − 65 = 115°.
3. 45 + 80 = 125, so x = 180 − 125 = 55°.
4. x = 180 − 90 = 90°.
5. 115 + 25 = 140, so x = 180 − 140 = 40°.
Answer to Question 4
1. 110 + 90 + 75 = 275. x = 360 − 275 = 85°.
2. x = 360 − 200 = 160°.
3. 120 + 120 = 240. x = 360 − 240 = 120°.
4. 45 + 135 + 90 = 270. x = 360 − 270 = 90°.
5. 35 + 85 + 140 = 260. x = 360 − 260 = 100°.
Answer to Question 5
1. Count the sides of each shape: the first has 5 sides, the second 6 and the third 8. The answer is pentagon, hexagon, octagon.
2. Any polygon with four straight sides is called a quadrilateral (squares, rectangles and kites are all quadrilaterals).
3. Three straight sides and three vertices make a triangle.
4. The prefix “deca” means ten, as in decade. A 10-sided polygon is a decagon.
5. A seven-sided shape is a heptagon; the 50p and 20p coins are based on this shape.
Answer to Question 6
1. A regular polygon has all its sides equal, so perimeter = number of sides × side length. A hexagon has 6 sides: 6 × 6 = 36 cm.
2. An octagon has 8 equal sides: 8 × 4 = 32 cm.
3. A pentagon has 5 equal sides: 5 × 9 = 45 cm.
4. An equilateral triangle has 3 equal sides: 3 × 12 = 36 cm.
5. Work backwards: the 10 equal sides share the perimeter, so 80 ÷ 10 = 8 cm. Check: 10 × 8 = 80.
Answer to Question 7
1. 360 ÷ 12 = 30°.
2. At 3 o'clock the hands are 3 hours apart: 3 × 30 = 90°, a right angle.
3. 6 hours apart: 6 × 30 = 180°, a straight line.
4. 4 hours apart: 4 × 30 = 120°, obtuse.
5. 15 minutes is a quarter of an hour: 360 ÷ 4 = 90°.
Answer to Question 8
1. It has 8 sides. All the sides are equal and all the angles are equal because it is regular.
2. 8 × 25 = 200 cm (2 m).
3. 195 ÷ 3 = 65 cm.
4. 12 × 200 cm = 2,400 cm = 24 m.
Answer to Question 9
1. The angles at the centre make a full turn of 360°, shared equally between 8 slices: 360 ÷ 8 = 45°.
2. Shared between 6 slices: 360 ÷ 6 = 60°.
3. Shared between 12 slices: 360 ÷ 12 = 30°, like the angle between two numbers on a clock face.
4. Each slice is 45°, so 3 slices make 3 × 45 = 135°. The rest of the pizza is 360 − 135 = 225° (5 slices × 45°).
Answer to Question 10
1. Add the turns: 90 + 90 = 180°. That is a half turn, a straight angle, so the robot now faces the opposite way.
2. A quarter turn is 90°, so three quarters is 3 × 90 = 270°.
3. 180° is a half turn, which points the opposite way. The opposite of north is south.
4. A full turn is 360°. The missing part is 360 − 270 = 90°, one more quarter turn.
Answer to Question 11
1. The two angles sit on a straight line (the fence), and angles on a straight line add up to 180°. So x = 180 − 130 = 50°.
2. The gate moves 20° towards the side of x, so x shrinks by 20°: 50 − 20 = 30°. (The other angle grows to 150°; 150 + 30 = 180.)
3. A right angle is 90°, and 180 − 90 = 90, so the angle is 90° on both sides.
4. Again the angles on the straight fence add up to 180°: y = 180 − 75 = 105°.
Answer to Question 12
1. A 90° clockwise turn from north takes her to the next compass point, east.
2. 180° is a half turn, so she faces the opposite direction. The opposite of east is west.
3. Clockwise from north: 90° to east, 180° to south, 270° to west. The answer is 270° (or 90° anticlockwise).
4. Anticlockwise from south: 90° brings her to east, 180° to north and 270° to west.
Answer to Question 13
1. A hexagon has 6 sides and the perimeter is 6 × 3 = 18 cm.
2. 360 ÷ 3 = 120°.
3. Two hexagons have 12 sides in total. They share 1 side, so 12 − 2 = 10 sides are on the outside.
4. 10 × 3 = 30 cm.
Answer to Question 14
1. A decagon has 10 sides.
2. 10 × 1.5 = 15 m.
3. 15 ÷ 5 = 3 tins.
4. Square: 4 × 2 = 8 m. Triangle: 3 × 3 = 9 m. Total: 15 + 8 + 9 = 32 m.
Answer to Question 15
1. 5 sides. Perimeter = 5 × 8 = 40 m.
2. 40 − 2 = 38 m.
3. 38 × 12 = £456.
4. The hexagon has 6 sides and the same perimeter of 40 m. 40 ÷ 6 = 6 remainder 4, so each side is 6 2/3 m (about 6.67 m).
5. The five angles at the centre are equal and add to 360°: 360 ÷ 5 = 72°.
Answer to Question 16
1. a = 180 − 65 = 115°.
2. The angles add to 180°: 30 + b + 2b = 180, so 3b = 150 and b = 50°. (The three angles are 30°, 50° and 100°.)
3. 90 + 80 = 170 and 360 − 170 = 190. Two equal angles: 190 ÷ 2 = 95° each.
4. 100 + d + 3d = 360, so 4d = 260 and d = 65°. Then 3d = 195°.
5. Acute: b = 50° and d = 65°. Obtuse: a = 115°, 2b = 100° and c = 95°. Reflex: 3d = 195°.
Answer to Question 17
1. Stop sign: 8 × 30 = 240 cm. Warning sign: 3 × 90 = 270 cm.
2. 25 × 240 = 6,000 cm = 60 m.
3. 20 × 270 = 5,400 cm = 54 m.
4. 60 + 54 = 114 m. 114 × £2 = £228.
5. Stop signs need 60 m and warning signs need 54 m. Stop signs need 6 m more.
Answer to Question 18
1. 4 corners: 360 ÷ 4 = 90°.
2. 5 corners: 360 ÷ 5 = 72°.
3. 6 corners: 360 ÷ 6 = 60°.
4. 360 ÷ 40 = 9 sides, a regular nonagon.
5. The square (90°). The more sides a polygon has, the smaller the turn at each corner.
Answer to Question 19
1. C is scalene because all three sides are different lengths.
2. A and D have three equal sides.
3. B has exactly two equal sides.
4. A: 15 cm. B: 6 + 6 + 4 = 16 cm. C: 7 + 5 + 4 = 16 cm. D: 24 cm.
5. A regular hexagon with side 4 cm has perimeter 6 × 4 = 24 cm, so triangle D matches.
Answer to Question 20
1. 180 ÷ 45 = 4 steps.
2. 360 ÷ 45 = 8 steps.
3. 5 × 45 = 225°, which is a reflex angle.
4. 7 × 45 = 315°, also reflex.
5. 315 ÷ 45 = 7 steps. It still has to turn 360 − 315 = 45°.
Answer to Question 21
1. Inside angle = 180 − 60 = 120°.
2. Outside turn: 360 ÷ 8 = 45°. Inside angle: 180 − 45 = 135°.
3. Square: outside 90°, inside 180 − 90 = 90°. Triangle: outside 120°, inside 180 − 120 = 60°.
4. Three corners meet at the point: 3 × 120 = 360°, a full turn, so they fit with no gaps.

How to use these Year 5 angles and polygons worksheet answers

First, try every question on the worksheet without looking. Then compare your working with the solution line by line, not only the final answer. When your answer is different, find the first step that changes, because that is where the mistake is. After that, read the matching part of the angles and polygons lesson again. Finally, check that the method is secure with the quiz or the test.

Also, the Year 5 angles and polygons worksheet answers are available as a PDF, so you can mark printed work quickly. Moreover, all the pages of this chapter work together, so you can move between them at any time. For example, many pupils read the lesson on Monday, practise on Wednesday and test themselves on Friday. In short, these Year 5 angles and polygons worksheet answers show every step, so nothing is left unexplained.