📐 Angle Ace: Master Every Angle! 🎯

Angles are everywhere — in buildings, art, sport and navigation. In Grade 6, you'll classify angles, use angle rules to find missing angles, and understand why angles in shapes always add up to special totals. Become an Angle Ace and you'll never be stuck on a geometry problem again!

📏 Angle Types
Acute: <90°  ·  Right: 90°  ·  Obtuse: 90°–180°  ·  Reflex: >180°
⬆️ Angles on a Line
a + b = 180° (straight line)  ·  a + b + c + d = 360° (full turn)
🔺 Angles in Shapes
Triangle: sum = 180°  ·  Quadrilateral: sum = 360°

Angle Types

Acute

0° < x < 90°
e.g. 45°, 73°

Right

x = 90°
Exactly 90°

Obtuse

90° < x < 180°
e.g. 120°, 145°

Reflex

180° < x < 360°
e.g. 270°

Golden Rules

📏 Acute angle: greater than 0° and less than 90°. E.g., 45°, 73°.

📐 Right angle: exactly 90°. Shown with a small square in the corner.

📏 Obtuse angle: greater than 90° and less than 180°. E.g., 120°, 145°.

🔄 Reflex angle: greater than 180° and less than 360°. E.g., 270°.

➖ Angles on a straight line add up to 180°.

🔵 Angles around a point (full turn) add up to 360°.

✖️ Vertically opposite angles are EQUAL (formed where two straight lines cross).

🔺 Angles in a triangle sum to 180°.

🔷 Angles in any quadrilateral sum to 360°.

🔍 To find a missing angle: use the angle rule for that situation, then subtract the known angles from the total.

Triangle: a + b + c = 180° Quadrilateral: a + b + c + d = 360°
Collins Stage 6 Cambridge Primary Maths · Unit 20: Angles · FractionRush

📖 Worked Examples

Example 1: Angles on a Straight Line

Two angles on a straight line are 47° and x°. Find x.

47° x°
📌 Angles on a straight line = 180°
➕ x = 180° − 47°
✅ x = 133°
🏷️ x is obtuse ✓ (between 90° and 180°)

Example 2: Angles Around a Point

Three angles around a point are 125°, 90° and y°. Find y.

125° 90° y°
📌 Angles around a point = 360°
➕ y = 360° − 125° − 90°
✅ y = 145°
🏷️ y is obtuse ✓

Example 3: Missing Angle in a Triangle

A triangle has angles 64°, 73° and p°. Find p.

p° 64° 73°
📌 Angles in a triangle = 180°
➕ p = 180° − 64° − 73°
✅ p = 43°
🏷️ p is acute ✓

Example 4: Angles in a Quadrilateral

A quadrilateral has angles 95°, 110°, 75° and q°. Find q.

95° 110° 75° q°
📌 Angles in a quadrilateral = 360°
➕ q = 360° − 95° − 110° − 75°
✅ q = 80°
🏷️ q is acute ✓
Collins Stage 6 Cambridge Primary Maths · Unit 20: Angles · FractionRush

🔬 Missing Angle Calculator

Select the angle rule, enter the known angles, and find the missing one!

Collins Stage 6 Cambridge Primary Maths · Unit 20: Angles · FractionRush

🎯 Drag Exercise 1: Angle Types

Drag the correct angle type to the drop zone!

An angle measuring 127° is called a...?

Acute
Right
Obtuse
Reflex
127° is an
?
angle
💡 Hint: Obtuse angles are between 90° and 180°. Is 127° in that range?
Collins Stage 6 Cambridge Primary Maths · Unit 20: Angles · FractionRush

🎯 Drag Exercise 2: Straight Line

Find the missing angle on a straight line!

One angle on a straight line is 68°. What is the other angle?

68° ?°
102°
112°
122°
132°
The missing angle is
?
💡 Hint: Angles on a straight line = 180°.   180° − 68° = ?
Collins Stage 6 Cambridge Primary Maths · Unit 20: Angles · FractionRush

🎯 Drag Exercise 3: Full Turn

Find the missing angle around a point!

Angles of 130°, 95° and x° meet at a point. Find x.

130° 95° x°
125°
130°
135°
140°
x =
?
💡 Hint: Angles around a point = 360°.   360° − 130° − 95° = ?
Collins Stage 6 Cambridge Primary Maths · Unit 20: Angles · FractionRush

🎯 Drag Exercise 4: Triangle

Find the missing angle in a triangle!

A triangle has angles 52° and 81°. Find the third angle.

?° 52° 81°
37°
47°
57°
67°
Third angle =
?
💡 Hint: Angles in a triangle = 180°.   180° − 52° − 81° = ?
Collins Stage 6 Cambridge Primary Maths · Unit 20: Angles · FractionRush

🎯 Drag Exercise 5: Vertically Opposite

Find the vertically opposite angle!

Two straight lines cross. One angle is 63°. What is the vertically opposite angle?

63° ?° 117° 117°
117°
63°
27°
180°
Vertically opposite angle =
?
💡 Hint: Vertically opposite angles are EQUAL!
Collins Stage 6 Cambridge Primary Maths · Unit 20: Angles · FractionRush

🎯 Drag Exercise 6: Quadrilateral

Find the missing angle in a quadrilateral!

A quadrilateral has angles 100°, 85°, 75° and y°. Find y.

100° 85° 75° y°
90°
100°
110°
120°
y =
?
💡 Hint: Angles in a quadrilateral = 360°.   360° − 100° − 85° − 75° = ?
Collins Stage 6 Cambridge Primary Maths · Unit 20: Angles · FractionRush

✏️ Practice Questions

Try all 20 questions, then reveal the answers!

  1. Classify an angle of 45°.
  2. Classify an angle of 180°.
  3. Classify an angle of 250°.
  4. Two angles on a straight line are 54° and x°. Find x.
  5. Two angles on a straight line are 117° and y°. Find y.
  6. Angles around a point: 120°, 80°, 90° and a°. Find a.
  7. Find the missing angle in a triangle with angles 60° and 60°.
  8. A right-angled triangle has one angle of 35°. Find the third angle.
  9. A quadrilateral has angles 80°, 100°, 90° and p°. Find p.
  10. Two straight lines cross. One angle is 44°. Find all four angles.
  11. An isosceles triangle has a base angle of 72°. Find the apex angle.
  12. Find the missing angle: triangle with angles 90° and 47°.
  13. A quadrilateral has angles 70°, 110°, 70° and q°. Find q.
  14. One angle in an equilateral triangle is ___°.
  15. Angles on a straight line: 3 angles of 40°, 55° and z°. Find z.
  16. A reflex angle and its non-reflex partner together make ___°.
  17. An angle of 90° is bisected. What size is each half?
  18. A quadrilateral has three equal angles of 85° each. Find the fourth.
  19. Two angles are supplementary (add to 180°). One is 3 times the other. Find both.
  20. Interior angles of a regular hexagon each measure ___°.

Answers

  1. Acute (less than 90°)
  2. Straight angle (exactly 180°)
  3. Reflex (greater than 180°)
  4. x = 180° − 54° = 126°
  5. y = 180° − 117° = 63°
  6. a = 360° − 120° − 80° − 90° = 70°
  7. Missing angle = 180° − 60° − 60° = 60° (equilateral triangle)
  8. Third angle = 180° − 90° − 35° = 55°
  9. p = 360° − 80° − 100° − 90° = 90°
  10. Angles are 44°, 136°, 44°, 136° (vertically opposite pairs)
  11. Apex angle = 180° − 72° − 72° = 36°
  12. Missing angle = 180° − 90° − 47° = 43°
  13. q = 360° − 70° − 110° − 70° = 110°
  14. 60° (all angles in an equilateral triangle are equal)
  15. z = 180° − 40° − 55° = 85°
  16. 360° (reflex + non-reflex = full turn)
  17. 45° each
  18. Fourth angle = 360° − (3 × 85°) = 360° − 255° = 105°
  19. Let smaller angle = x; 3x + x = 180°; 4x = 180°; x = 45° and 3x = 135°
  20. Sum of interior angles = (6 − 2) × 180° = 720°; each angle = 720° ÷ 6 = 120°
Collins Stage 6 Cambridge Primary Maths · Unit 20: Angles · FractionRush

🏆 Challenge Problems

10 tougher problems to push your angle skills further!

  1. A triangle has angles in the ratio 1:2:3. Find all three angles.
  2. The exterior angle of a triangle is 115°. The two non-adjacent interior angles are equal. Find them.
  3. A regular polygon has interior angles of 144°. How many sides does it have?
  4. In a diagram, two parallel lines are cut by a transversal. One angle is 70°. Find the co-interior angle.
  5. A triangle has angles x°, 2x° and 3x°. Find x and classify the triangle.
  6. The angles of a quadrilateral are in ratio 2:3:4:3. Find all four angles.
  7. A clock shows 3 o'clock. What angle do the hands make?
  8. A clock shows 5 o'clock. What angle do the minute and hour hands make?
  9. An isosceles triangle has an apex angle of 40°. Find the base angles and state whether the triangle is acute, right-angled or obtuse.
  10. A straight line is divided into 5 equal angles. What is the size of each?

Answers

  1. Total parts = 1+2+3 = 6; each part = 180°÷6 = 30°; angles = 30°, 60°, 90° — a right-angled triangle!
  2. Interior angle at the exterior = 180° − 115° = 65°; the other two interior angles = (180° − 65°) ÷ 2 = 57.5° each
  3. Exterior angle = 180° − 144° = 36°; number of sides = 360° ÷ 36° = 10 sides (decagon)
  4. Co-interior angles sum to 180°; co-interior angle = 180° − 70° = 110°
  5. x + 2x + 3x = 180°; 6x = 180°; x = 30°; angles = 30°, 60°, 90° — right-angled scalene triangle
  6. Total parts = 2+3+4+3 = 12; each part = 360°÷12 = 30°; angles = 60°, 90°, 120°, 90°
  7. 90° (the hands are at a right angle at 3 o'clock)
  8. Each hour = 30°; 5 × 30° = 150°
  9. Base angles = (180° − 40°) ÷ 2 = 70° each. All angles are less than 90°, so the triangle is acute.
  10. 180° ÷ 5 = 36° each
Collins Stage 6 Cambridge Primary Maths · Unit 20: Angles · FractionRush