EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Exam Practice: Angle Properties
Angle properties of triangles and quadrilaterals · Angles and trigonometry · Lesson 1 of 7 · 10 marks · 20 minutes
Name Date
Answer all questions. Show your working. All questions are non-calculator.
Question 1 NON-CALCULATOR [2 marks]
In triangle PQR, PQ = PR and angle QPR = 52°. Work out the size of angle PQR.
Question 2 NON-CALCULATOR [3 marks]
AB and CD are parallel lines. The line EF crosses AB at P and CD at Q. Angle APQ = 65°. Work out the size of angle x. Give a reason for each stage of your working.
Question 3 NON-CALCULATOR [3 marks]
The angles of a quadrilateral are x, 2x, x + 30 and 2x + 30, in degrees. Work out the value of x. Then write down the size of the smallest angle.
Question 4 NON-CALCULATOR [2 marks]
Kim says, "A parallelogram with a right angle must be a square." Is Kim right? Give a reason for your answer.
Answers
Check your answer only once you have written one.
Question 1 [2 marks]
180 − 52 = 128, 128 ÷ 2 = 64. Angle PQR = 64°.
▸ 180 − 52, or 128 M1
▸ 64° A1
Question 2 [3 marks]
Angle APQ and angle x (angle PQC) are co-interior, so x = 180 − 65 = 115°. (Or: angle PQD = 65° because alternate angles are equal, then x = 180 − 65 = 115° because angles on a straight line add up to 180°.)
▸ x = 115 B1
▸ A correct reason, e.g. co-interior angles add up to 180°, or alternate angles are equal C1
▸ A full set of correct reasons for their method C1
Question 3 [3 marks]
x + 2x + x + 30 + 2x + 30 = 360, so 6x + 60 = 360, 6x = 300, x = 50. The smallest angle is x = 50°.
▸ Adding the four angles and setting equal to 360 M1
▸ 6x + 60 = 360 solved correctly as far as 6x = 300 M1
▸ x = 50, smallest angle 50° A1
Question 4 [2 marks]
No. A parallelogram with one right angle has four right angles, so it is a rectangle - but its sides need not all be equal, so it need not be a square.
▸ No, with an argument about the sides C1
▸ A counter-example, e.g. a rectangle 2 cm by 5 cm C1