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Singapore Primary Maths

Primary 5 Foundation maths · Geometry · About 12 minutes

Find unknown angles

Locate the common vertex, the given lines and the complete turn being filled.

Start the interactive lesson →Open practice activity

What you will learn

Models used: number sentences, stories, tables.

Before you start

Use the turn you already know

A straight line makes a half-turn. That whole turn is 180 degrees.

  1. The straight line is the whole half-turn. The coloured arcs show its two parts.

    A straight line makes a half-turn. That whole turn is 180 degrees.

    The unknown angle must fill exactly the part of the straight turn that the known angle does not use.

    60°?One straight turn = 180°
  2. The straight line is the whole half-turn. The coloured arcs show its two parts.

    The blue part uses 60 degrees. The orange part must fill the space left over.

    The unknown angle must fill exactly the part of the straight turn that the known angle does not use.

    60°?One straight turn = 180°
  3. The straight line is the whole half-turn. The coloured arcs show its two parts.

    Subtract the known part from the whole turn.

    180° − 60° = 120°

    The unknown angle must fill exactly the part of the straight turn that the known angle does not use.

    60°120°One straight turn = 180°
What did the picture help us see?

Subtract the known part from the whole turn.

Worked example: A new example, together

Angles 90° and x° make a full turn about a point. Find x.

Use the marked relationship
Known angleRelationship
90°360° total
  1. Use the marked relationship. Read each value with the heading above its column.

    Locate the common vertex, the given lines and the complete turn being filled.

    The component angles exactly fill 360 degrees.

    Use the marked relationship
    Known angleRelationship
    90°360° total
  2. Use the marked relationship. Read each value with the heading above its column.

    The complete turn here is 360°.

    Use the marked relationship
    Known angleRelationship
    90°360° total
    Angles 90° and x° make a full turn about a point. Find x.

    270 degrees

  3. Use the marked relationship. Read each value with the heading above its column.

    Subtract the known angle: 360 − 90.

    Use the marked relationship
    Known angleRelationship
    90°360° total
  4. Use the marked relationship. Read each value with the heading above its column.

    x = 270°.

    Use the marked relationship
    Known angleRelationship
    90°360° total
  5. Use the marked relationship. Read each value with the heading above its column.

    Check the result against the question we started with.

    90 + 270 = 360°.

    We found 270 degrees. The component angles exactly fill 360 degrees.

    Use the marked relationship
    Known angleRelationship
    90°360° total

Common mistakes to discuss

Check your understanding

Explain your reasoning to an adult, then try a fresh question in the interactive lesson. A result from one attempt is not proof of lasting mastery.

Try this lesson →

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