KS3 & KS4 Maths Diagnostic questions

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Angle facts

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  1. ang-01 Present from here

    The diagram shows a straight line. What is the size of angle $x$?

    A straight line with a ray from a point on it. The angles either side of the ray are 35 degrees and x.
    Option A: $325^\circ$
    Option B: $35^\circ$
    Option C: $145^\circ$
    Option D: $55^\circ$
    Answer and misconceptions
    Option A: $325^\circ$ ✗
    Uses 360° for angles on a straight lineCalculates 360 − 35, mixing up angles on a line with angles around a point.
    Option B: $35^\circ$ ✗
    Assumes the two angles are equalTreats the angles as if they were vertically opposite, so gives 35°.
    Option C: $145^\circ$ ✓ Correct
    Option D: $55^\circ$ ✗
    Uses 90° for angles on a straight lineCalculates 90 − 35, confusing a straight line with a right angle.
  2. ang-02 Present from here

    Three lines meet at a point. What is the size of angle $x$?

    Three lines meeting at a point, making angles of 70 degrees, 80 degrees and x all the way round.
    Option A: $210^\circ$
    Option B: $30^\circ$
    Option C: $150^\circ$
    Option D: $120^\circ$
    Answer and misconceptions
    Option A: $210^\circ$ ✓ Correct
    Option B: $30^\circ$ ✗
    Uses 180° for angles around a pointCalculates 180 − 70 − 80, using the straight-line total instead of 360°.
    Option C: $150^\circ$ ✗
    Thinks x equals the sum of the other two anglesAdds 70 + 80 and stops, as if x were equal to the sum of the known angles.
    Option D: $120^\circ$ ✗
    Assumes angles around a point are equalDivides 360 by 3, ignoring the given angles.
  3. ang-03 Present from here

    Two straight lines cross. What is the size of angle $x$?

    Two straight lines crossing. One angle is 48 degrees and the angle opposite it is x.
    Option A: $132^\circ$
    Option B: $312^\circ$
    Option C: $42^\circ$
    Option D: $48^\circ$
    Answer and misconceptions
    Option A: $132^\circ$ ✗
    Treats opposite angles as on a straight lineCalculates 180 − 48, using the rule for adjacent angles instead of vertically opposite angles.
    Option B: $312^\circ$ ✗
    Subtracts from 360° for opposite anglesCalculates 360 − 48, thinking the two opposite angles make a full turn.
    Option C: $42^\circ$ ✗
    Confuses vertically opposite with complementaryCalculates 90 − 48, confusing vertically opposite with complementary angles.
    Option D: $48^\circ$ ✓ Correct
  4. ang-04 Present from here

    The two horizontal lines are parallel. What is the size of angle $x$?

    Two parallel lines crossed by a sloping line. At the top line the angle between the parallels on the right of the sloping line is 70 degrees. At the bottom line the angle between the parallels on the same side is x.
    Option A: $70^\circ$
    Option B: $110^\circ$
    Option C: $290^\circ$
    Option D: $20^\circ$
    Answer and misconceptions
    Option A: $70^\circ$ ✗
    Thinks co-interior angles are equalTreats these as alternate or corresponding angles; co-interior angles add to 180°.
    Option B: $110^\circ$ ✓ Correct
    Option C: $290^\circ$ ✗
    Thinks co-interior angles add to 360°Calculates 360 − 70 instead of 180 − 70.
    Option D: $20^\circ$ ✗
    Thinks co-interior angles add to 90°Calculates 90 − 70, using a right angle as the total.
  5. ang-05 Present from here

    What is the size of angle $x$ in this triangle?

    A right-angled triangle. The right angle is marked with a square. Another angle is 35 degrees and the third angle is x.
    Option A: $145^\circ$
    Option B: $235^\circ$
    Option C: $55^\circ$
    Option D: $35^\circ$
    Answer and misconceptions
    Option A: $145^\circ$ ✗
    Ignores the right-angle markerCalculates 180 − 35, not counting the 90° shown by the square.
    Option B: $235^\circ$ ✗
    Uses 360° for angles in a triangleCalculates 360 − 90 − 35, using the quadrilateral total.
    Option C: $55^\circ$ ✓ Correct
    Option D: $35^\circ$ ✗
    Assumes the two acute angles are equalThinks the triangle is isosceles, so x matches the 35° angle.
  6. ang-06 Present from here

    Three angles, $3x$, $2x$ and $x$, lie together on a straight line. What is the value of $x$?

    Option A: $60$
    Option B: $30$
    Option C: $36$
    Option D: $90$
    Answer and misconceptions
    Option A: $60$ ✗
    Uses $360^\circ$ for angles on a straight lineWrites $6x = 360$; angles on a straight line add up to $180^\circ$, so $6x = 180$.
    Option B: $30$ ✓ Correct
    Option C: $36$ ✗
    Does not count $x$ as $1x$ when collecting termsAdds $3x + 2x = 5x$ and leaves out the lone $x$, so solves $5x = 180$.
    Option D: $90$ ✗
    Gives the largest angle instead of $x$Finds $x = 30$ correctly, then gives $3x = 90$ as the answer.