QUESTION 3 · Shapes & Angles

Reason with Angles

Choose an angle fact and explain every deduction.

DISCOVER · PREDICT BEFORE YOU CHANGE

Make the relationship visible

65°b

Blue sector: given angle. Orange sector: b. Parallel arrows justify the selected relationship; b = 115°.

Predict b before moving the slider. Identify the positions of both marked sectors.

CHOOSE AN INDIVIDUAL ACTION

Read and use angle facts

Read three-letter angle names and use straight-line, full-turn and opposite-angle facts.

6 stages48 mixed itemsSee exam connections

Check Your Skill Level

All 48 canonical questions for this skill, grouped by stage. Use this printable check to find where review is needed.

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YOUR SKILL LADDER

Read and use angle facts

0/6 mastered
Before you start

Subtract from 180° and 360°; the middle letter names the vertex.

Already secure with these actions? Open any stage directly.

SHORT TUTORIAL

  1. 1

    Identify the vertex and the relationship before doing arithmetic.

  2. 2

    Read exactly what is stated. Separate guaranteed facts from appearance.

  3. 3

    A straight angle is 180°; a full turn is 360°; vertically opposite angles are equal.

COACH · ANTICIPATE EACH DECISION

In ∠ABC, which letter names the vertex?

Before revealing: which property or operation will you use?

    Watch for this: Adjacent angles are not always equal, and opposite-looking angles may not be vertically opposite.

    MIXED PRACTICE · 8 ITEMS

    Practise. Explain. Check.

    Show your working or construction on paper. State units where asked. For questions 7 and 8, explain your method. Numerical entries may be rounded to 2 decimal places. Later stages retrieve earlier methods. Answers and explanations stay separate.

    See answers & explanations
    1. Q

      The middle letter in a three-letter angle name names the vertex.

    2. M

      The middle letter in a three-letter angle name names the vertex.

    3. Y

      The middle letter in a three-letter angle name names the vertex.

    4. E

      The middle letter in a three-letter angle name names the vertex.

    5. S

      The middle letter in a three-letter angle name names the vertex.

    6. B

      The middle letter in a three-letter angle name names the vertex.

    7. Q

      The middle letter in a three-letter angle name names the vertex.

    8. M

      The middle letter in a three-letter angle name names the vertex.

    Self-assess only after at least 7 of 8 independently, including both reasoning items. At stages 4–6, explain a method choice. Before calling the whole skill secure, solve two unseen variants including another context. Repeat after several days. These are teaching targets.

    Use this skill somewhere else

    Connect it to another action, then solve a fresh problem without a method cue.

    Reason with parallel lines Derive polygon angles

    Mastery choices are saved in this browser on this device. Numerical checks and reason choices are shown separately. Paper drawings and constructions need your own or your teacher’s review.