Two parallel lines are cut by a transversal. Angle a is vertically opposite to a given angle of 60 degrees. Work out the size of angle a.
(a)Work out the size of angle a.(2)
(Total for Question 1 is 2 marks)
2
Lines l and m are parallel. A transversal cuts them. An angle labelled b on line l is 110 degrees and is interior on the same side of the transversal as angle c on line m. Work out angle c.
(a)Work out the size of angle c. Give a brief reason.(3)
(Total for Question 2 is 3 marks)
3
A pair of parallel lines is cut by a transversal. Angle d is corresponding to a given angle of 35 degrees. Work out angle d.
(a)Work out the size of angle d.(2)
(Total for Question 3 is 2 marks)
4
Two parallel lines are cut by a transversal. At the upper intersection one acute angle is 48 degrees. Find the obtuse angle e at the lower intersection which is co-interior with the 48 degree angle.
(a)Work out the size of angle e. Give a short reason.(4)
(Total for Question 4 is 4 marks)
5
A transversal crosses two parallel lines. At the top intersection an exterior angle f is 130 degrees. At the lower intersection the interior adjacent angle g is next to f on the same side of the transversal. Work out the size of angle g, then explain briefly why your answer is correct.
(a)Work out the size of angle g.(3)
(b)Give a brief reason for your answer to part (a).(2)
(Total for Question 5 is 5 marks)
6
A transversal meets two parallel lines. Angle h at the top left intersection is 27 degrees. Angle j at the bottom right intersection is vertically opposite to an angle corresponding to h. Work out angle j.
(a)Work out the size of angle j. Show your reasoning in two short steps.(5)
(Total for Question 6 is 5 marks)
7
In the diagram two parallel lines are cut by a transversal. Angle p at the top right is 62 degrees. At the lower intersection there are four labelled angles: r (lower left), s (lower right), t (upper right) and u (upper left).
(a)Work out the size of angle t. (2 marks)(2)
(b)Work out the sizes of r and s. Show the steps. (4 marks)(4)
(Total for Question 7 is 6 marks)
8
A student is given the diagram of two parallel lines cut by a transversal. At the top intersection angle m is 44 degrees. At the lower intersection three angles are labelled: x (upper left), y (upper right) and z (lower right).
(a)Work out the size of x. Give a short reason. (6 marks)(6)
(b)Work out the sizes of y and z. Show each step clearly. (7 marks)(7)
(Total for Question 8 is 13 marks)
Mark scheme · 4.10F Angles in Parallel Lines: Foundation Tier Practice
Question 1
(a) B1 identify vertically opposite angles are equal or state a = 60 degrees
(a) B1 final answer 60 degrees cao
(a) Answer: 60 degrees
Question 2
(a) M1 identify that co-interior angles sum to 180 degrees (supplementary) or state relation
(a) A1 70 degrees cao
(a) B1 reason: co-interior angles sum to 180 degrees oe
(a) Answer: 70 degrees
Question 3
(a) B1 identify corresponding angles are equal or state d = 35 degrees
(a) B1 final answer 35 degrees cao
(a) Answer: 35 degrees
Question 4
(a) M1 identify co-interior angles sum to 180 degrees or state relation
(a) M1 compute 180 - 48 = 132
(a) A1 132 degrees cao
(a) B1 reason: co-interior angles on the same side of the transversal sum to 180 degrees oe
(a) Answer: 132 degrees
Question 5
(a) M1 recognise that exterior angle 130 corresponds to an obtuse interior or use supplementary relation depending on position
(a) M1 compute 180 - 130 = 50 or identify equal alternate/corresponding relation as appropriate
(a) A1 50 degrees cao
(a) Answer: 50 degrees
(b) B1 state that interior and exterior angles on a straight line sum to 180 degrees or that corresponding angles are equal, making g = 50 degrees
(b) B1 final statement linking the two intersections via parallel lines (e.g. corresponding angles equal or co-interior supplementary)
(b) Answer: Because the interior and exterior angles on a straight line sum to 180 degrees, and corresponding positions on parallel lines are equal, so g = 180 - 130 = 50 degrees.
Question 6
(a) M1 identify that corresponding angle to h is equal to 27 degrees
(a) M1 identify that j is vertically opposite to that corresponding angle
(a) A1 state j = 27 degrees cao
(a) B1 give short reasoning e.g. corresponding angles equal and vertically opposite angles equal
(a) B1 final answer justified (explicit link: j = corresponding angle = h = 27 degrees)
(a) Answer: 27 degrees
Question 7
(a) M1 identify t corresponds to p or is equal to 62 degrees by corresponding/alternate reasoning
(a) A1 62 degrees cao
(a) Answer: 62 degrees
(b) M1 identify r is vertically opposite t (equal) or use relation r + u = 180 depending on chosen route
(b) M1 calculate u = 180 - t = 180 - 62 = 118 or state u = 118
(b) A1 r = 62 degrees cao
(b) A1 s = u = 118 degrees cao (s is vertically opposite u)
(b) Answer: r = 62 degrees, s = 118 degrees
Question 8
(a) M1 identify that x is corresponding to m (or alternate depending on orientation) so equal to 44 degrees
(a) M1 state equality: x = 44
(a) A1 44 degrees cao
(a) B1 give reason: corresponding angles are equal when lines are parallel
(a) B1 clarify link to the diagram (e.g. 'x is in the corresponding position to m')
(a) B1 final clear statement x = 44 degrees
(a) Answer: 44 degrees
(b) M1 identify that y is adjacent to x along the parallel line, so x and y are supplementary
(b) M1 compute y = 180 - 44 = 136 degrees
(b) M1 identify that z is vertically opposite to x on the straight line at the lower intersection
(b) M1 compute z = 44 degrees (equal to x, vertically opposite)
(b) A1 y = 136 degrees cao
(b) A1 z = 44 degrees cao
(b) B1 final statement linking steps clearly (e.g. 'x + y = 180 so y = 136, z is vertically opposite x so z = 44')