[discia] GCSE Maths › Geometry & Measures › Angles

Angles

discia.org 10 questions · 23 marks
Name Date
  1. Either paper 3 marks

    Here are the sizes of four angles.

    \(332^\circ\) · \(90^\circ\) · \(106^\circ\) · \(32^\circ\)

    One of them is a right angle.

    (a)

    State the size of the angle that is acute.

    (b)

    State the size of the angle that is obtuse.

    (c)

    State the size of the angle that is reflex.

    Show answer
    (a) \(32^\circ\)
    (b) \(106^\circ\)
    (c) \(332^\circ\)
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  2. Either paper 2 marks

    \(AOB\) is a straight line.

    \(OC\) and \(OD\) are two more straight lines drawn from \(O\), both on the same side of \(AOB\), with \(OC\) between \(OA\) and \(OD\).

    Angle \(AOC = 91^\circ\) and angle \(COD = 69^\circ\).

    Work out the size of angle \(DOB\).

    Show answer
    \(20^\circ\)
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  3. Either paper 2 marks

    \(OA\), \(OB\), \(OC\) and \(OD\) are four straight lines drawn from the point \(O\), arranged in that order all the way round \(O\).

    Angle \(AOB = 79^\circ\), angle \(BOC = 46^\circ\) and angle \(COD = 116^\circ\).

    Calculate the size of angle \(DOA\).

    Show answer
    \(119^\circ\)
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  4. Either paper 2 marks

    The diagram shows a triangle.

    48°72°xDiagram NOT accurately drawn

    Calculate the size of the angle marked \(x\).

    Show answer
    \(60^\circ\)
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  5. Either paper 1 mark

    The diagram is drawn accurately.

    x

    Estimate the size of the angle marked \(x\).

    You must not use a protractor.

    Show answer
    \(50^\circ\) — accept any answer from \(40^\circ\) to \(60^\circ\)
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  6. Either paper 2 marks

    Here is a right-angled triangle.

    35°xDiagram NOT accurately drawn

    Find the size of the angle marked \(x\).

    Show answer
    \(55^\circ\)
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  7. Either paper 4 marks

    Two straight lines \(AB\) and \(CD\) cross at the point \(O\).

    Angle \(AOC = 140^\circ\).

    (a)

    Write down the size of angle \(BOD\), and give a reason for your answer.

    (b)

    Find the size of angle \(AOD\), and give a reason for your answer.

    Show answer
    (a) \(BOD = 140^\circ\), because vertically opposite angles are equal
    (b) \(AOD = 40^\circ\), because angles on a straight line add up to 180 degrees
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  8. Either paper 2 marks

    The diagram shows an isosceles triangle.

    x116°

    Work out the size of the angle marked \(x\).

    Show answer
    \(32^\circ\)
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  9. Either paper 2 marks

    Here is an isosceles triangle.

    59°x

    Work out the size of the angle marked \(x\).

    Show answer
    \(62^\circ\)
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  10. Either paper 3 marks

    Here is triangle \(ABC\). The side \(AB\) is continued to the point \(D\).

    ABC82°54°Dx
    (a)

    Work out the size of the angle marked \(x\).

    (b)

    A student says that an angle of \(156^\circ\) is an acute angle.

    The student is wrong. Explain why.

    Show answer
    (a) \(136^\circ\)
    (b) \(156^\circ\) is between 90° and 180°, so it is an obtuse angle. Acute angles are less than 90°.
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discia.org Angles · sheet 1
Answers Angles · sheet 1
  1. (a) \(32^\circ\)
    (b) \(106^\circ\)
    (c) \(332^\circ\)
  2. \(20^\circ\)
  3. \(119^\circ\)
  4. \(60^\circ\)
  5. \(50^\circ\) — accept any answer from \(40^\circ\) to \(60^\circ\)
  6. \(55^\circ\)
  7. (a) \(BOD = 140^\circ\), because vertically opposite angles are equal
    (b) \(AOD = 40^\circ\), because angles on a straight line add up to 180 degrees
  8. \(32^\circ\)
  9. \(62^\circ\)
  10. (a) \(136^\circ\)
    (b) \(156^\circ\) is between 90° and 180°, so it is an obtuse angle. Acute angles are less than 90°.
discia.org Angles · sheet 1