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Oak National Academy
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Year 8

Missing angles

I can solve problems that require a combination of angles facts to identify values of missing angles, providing explanations of reasoning and logic used.

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New
New
Year 8

Missing angles

I can solve problems that require a combination of angles facts to identify values of missing angles, providing explanations of reasoning and logic used.

Download all resources
Share activities with pupils

Lesson details

Key learning points

  1. Missing angles can be found using parallel lines.
  2. Missing angles can be found using facts about triangles.
  3. Missing angles can be found in polygons using knowledge of exterior and interior angles.
  4. The relationship between interior and exterior angles can be used to find missing angles.
  5. Missing angles can be found by using a combination of all known facts.

Common misconception

Pupils may work out missing angles without writing out their justifications.

Each time a number which is not on the original diagram is used or found, an explanation should be given for where it has come from.

Keywords

  • Corresponding angles - A pair of angles at different vertices on the same side of a transversal in equivalent positions.

  • Alternate angles - A pair of angles both between or both outside two line segments that are on opposite sides of the transversal that cuts them.

  • Co-interior angles - Co-interior angles are on the same side of the transversal line and in between the two other lines.

  • Interior angles - An interior angle is an angle formed inside a polygon by two of its edges.

  • Exterior angle - An exterior angle is an angle on the outside of a polygon between an extension of an edge and its adjacent edge.

Many of the problems can be solved using multiple methods. Once a pupil has completed a problem, encourage them to consider how they might solve it in a different way or to compare their working with somebody else who has done it differently.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Starter quiz

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6 Questions

Q1.
In which cases are the angles always equal to each other?
adjacent angles on a straight line
Correct answer: alternate angles on parallel lines
co-interior angles on parallel lines
Correct answer: corresponding angles on parallel lines
Correct answer: vertically opposite angles
Q2.
Co-interior angles on parallel lines sum to °.
Correct Answer: 180, one hundred and eighty, 180°, one hundred and eighty degrees, a hundred and eighty
Q3.
Which angle is 97°?
An image in a quiz
Correct answer: ∠BCD
∠CBD
∠CDB
∠DBC
Q4.
Match each shape with the sum of its interior angles.
Correct Answer:decagon,1440°

1440°

Correct Answer:heptagon,900°

900°

Correct Answer:hexagon,720°

720°

Correct Answer:nonagon,1260°

1260°

Correct Answer:octagon,1080°

1080°

Correct Answer:pentagon,540°

540°

Q5.
∠ACE = ∠FEC because .
An image in a quiz
Correct answer: they are alternate angles on the parallel lines
they are corresponding angles on the parallel lines
they are vertically opposite angles
Q6.
Which angle is co-interior to ∠ACE?
An image in a quiz
∠BCA
Correct answer: ∠CEH
∠ECD
∠FEC
∠GEH

Exit quiz

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6 Questions

Q1.
∠ABG = 112°. Based on this information, which justification could be used to explain why ∠CBG = 68°?
An image in a quiz
Correct answer: Adjacent angles on a straight line sum to 180°.
Angles in a triangle sum to 180°.
Co-interior in parallel lines angles sum to sum to 180°.
Q2.
Which justification could be used to explain why ∠CGF = ∠GCD?
An image in a quiz
Correct answer: Alternate angles in parallel lines are equal.
Corresponding angles in parallel lines are equal.
Vertically opposite angles are equal.
Q3.
Match each statement with its justification.
An image in a quiz
Correct Answer:∠ECD = ∠CEH,alternate angles in parallel lines are equal

alternate angles in parallel lines are equal

Correct Answer:∠DCB = ∠FEC,corresponding angles in parallel lines are equal

corresponding angles in parallel lines are equal

Correct Answer:∠ACE = ∠DCB,vertically opposite angles are equal

vertically opposite angles are equal

Correct Answer:∠BCA and ∠ACE sum to 180°,adjacent angles on a straight line sum to 180°

adjacent angles on a straight line sum to 180°

Correct Answer:∠ECD and ∠FEC sum to 180°,co-interior angles in parallel lines sum to sum to 180°

co-interior angles in parallel lines sum to sum to 180°

Q4.
Given ∠EGC = 82°, then ∠CGB = °.
An image in a quiz
Correct Answer: 16, sixteen, sixteen degrees, 16°
Q5.
The pentagon in the image is regular. The size of the shaded angle is °.
An image in a quiz
Correct Answer: 36, 36°, thirty six, thirty six degrees
Q6.
The image shows a regular pentagon and a regular hexagon. The size of the shaded angle is °.
An image in a quiz
Correct Answer: 48, forty eight, forty eight degrees, 48°