Grade 6 MathsGeometry

Angle Lab

Name angles, sort them by size, measure them with a protractor, draw them, and use angle facts with lines and shapes to find missing angles.

Try it: drag the yellow dot to open or close the angle. Watch the size and the name change.

50°Acute

Lesson 1

Parts of an angle and how to name it

An angle is made when two rays start from the same point. The size of an angle tells us how much one ray has turned away from the other.

BCA vertex (corner point) arm BC (a ray) arm BA (a ray) ∠ABC
  • The vertex is the point where the two arms meet.
  • The arms are the two rays that make the angle.
  • We measure angles in degrees (°). One full turn is 360°.
  • The symbol ∠ means “angle”.

Three ways to name an angle

  1. Three letters, with the vertex in the middle: ∠ABC or ∠CBA. Both name the same angle.
  2. The vertex letter only: ∠B. Use this only when there is just one angle at B.
  3. A number or small letter written inside the angle: ∠1 or ∠x.

Why the middle letter matters: below, three angles share vertex B. Tap a name to see which angle it means. Saying “∠B” here would be confusing.

Lesson 2

Types of angles

We sort angles by comparing them with a right angle (90°, a square corner) and a straight angle (180°, a straight line).

Name that angle

Look at the angle shaded in coral. Estimate first: is it smaller than a square corner, exactly a square corner, or bigger? Then choose its type.

Quick check: hold the corner of a sheet of paper against the screen. If the angle fits inside the corner, it is acute.

Correct in a row: 0  ·  Best: 0

Lesson 3

Measuring an angle with a protractor

A protractor is a half circle marked from 0° to 180°. It has two scales that run in opposite directions. Here the outer scale is navy and the inner scale is coral.

  1. Estimate. Is the angle acute or obtuse? Your answer must match.
  2. Centre. Put the centre point of the protractor exactly on the vertex.
  3. Line up. Turn the protractor so the baseline (the 0° line) lies along one arm.
  4. Choose the scale that shows 0 on that arm.
  5. Read. Follow the same scale round to the other arm. Read the number where the arm crosses it.

Common mistake: reading the wrong scale. A 50° angle can look like 130° if you start from the 0 on the other side. Always check your estimate: acute angles are less than 90°.

In the lab: drag the blue protractor to move it. Drag the coral knob to turn it. It clicks into place when it is close.

Protractor lab

Centre on vertexBaseline on an arm
°
Lesson 4

Drawing an angle of a given size

You need a sharp pencil, a ruler and a protractor. Follow the steps and make the angle yourself.

Draw ∠ABC = 65°

  1. Draw the first arm. Use a ruler to draw a ray BC. Mark the vertex B.
  2. Place the protractor. Centre on B. Baseline along BC.
  3. Mark a dot. Find 65° on the scale that starts at 0 on BC. Tap that spot on the edge to make a dot.
  4. Join and label. Remove the protractor. Use the ruler to join B to the dot. Label the dot A.

Check your drawing. If you were asked for an acute angle, does your angle look smaller than a square corner?

Lesson 5

Angle pairs and angle facts

Adjacent angles share a vertex and an arm and sit side by side. When adjacent angles fill a right angle, a straight line or a full turn, we know their total.

  • Complementary angles add up to 90°. 30° and 60° are complementary.
  • Supplementary angles add up to 180°. Angles on a straight line are supplementary.
  • Angles around a point add up to 360°, one full turn.

Memory trick: C comes before S in the alphabet, and 90 comes before 180. Complementary makes a Corner. Supplementary makes a Straight line.

Drag the yellow dots

Two crossing lines

Drag the yellow dot

Vertically opposite angles

When two straight lines cross, they make four angles. The angles opposite each other (across the vertex) are always equal.

The angles next to each other sit on a straight line, so they add up to 180°.

So if you know one of the four angles, you can find all the others.

Lesson 6

Parallel lines, perpendicular lines and transversals

Lines on a flat surface either never meet or cross at one point. How they meet decides the angles.

A transversal is a line that crosses two or more other lines. It makes 8 angles, numbered here 1 to 8.

When the two lines are parallel:

  • Corresponding angles are equal. They are in the same position at each crossing. Look for an F shape.
  • Alternate interior angles are equal. They are between the lines, on opposite sides of the transversal. Look for a Z shape.
  • Alternate exterior angles are equal. They are outside the lines, on opposite sides.
  • Co-interior angles add up to 180°. They are between the lines, on the same side. Look for a C or U shape.

These rules only work when the lines are parallel. Tick “Tilt the bottom line” to see them break.

Lesson 7

Angles in triangles, quadrilaterals and diagonals

Drag the corners of each shape. The angles change, but the total stays the same.

Triangle

Acute triangle

Tear off the three corners and put them side by side. They always make a straight line:

Quadrilateral

A diagonal joins two corners that are not next to each other. One diagonal cuts a quadrilateral into two triangles, so its angles add to 2 × 180° = 360°.

Diagonals in polygons

Count the triangles

From one corner, draw every diagonal you can. Count the triangles. Each triangle gives 180°.

Rule: a polygon with n sides splits into n − 2 triangles, so its angles add up to (n − 2) × 180°. The total number of diagonals is n × (n − 3) ÷ 2.

Lesson 8

Find the missing angle

Diagrams are not drawn to scale, so do not measure. Use an angle fact, write a number sentence, then solve it.

90°

Complementary angles, a right angle

180°

Angles on a straight line; angles in a triangle; co-interior angles

360°

Angles around a point; angles in a quadrilateral

=

Vertically opposite, corresponding and alternate angles are equal

Lesson 9

Check your understanding

15 questions on everything in Angle Lab. You get feedback after each answer.