P, Q and R lie on a straight line. Angle a and an angle of 118 degrees lie on the same side of the line at Q.
Diagram NOT accurately drawn
(Total for Question 2 is 1 mark)
3
Lines l and m are parallel. A transversal crosses l and m. At the intersection with l, one of the angles formed is 105 degrees. Angle b, at the intersection with m, is in the corresponding position to the 105 degree angle.
Diagram NOT accurately drawn
(Total for Question 3 is 2 marks)
4
Lines l and m are parallel and are crossed by a transversal. One of the angles between the transversal and l is 71 degrees. Angle x, between the transversal and m, is in the alternate position to the 71 degree angle.
Diagram NOT accurately drawn
(Total for Question 4 is 2 marks)
5
Lines l and m are parallel and are crossed by a transversal. One of the angles between the transversal and l is 109 degrees. Angle y, between the transversal and m, is in the co-interior position to the 109 degree angle.
Diagram NOT accurately drawn
(Total for Question 5 is 2 marks)
6
Lines PQ and RS are parallel and are crossed by a transversal. One of the angles between the transversal and PQ is 118 degrees. Angle a, between the transversal and RS, is in the corresponding position to the 118 degree angle. Angle b, between the transversal and RS, is in the co-interior position to the 118 degree angle.
Diagram NOT accurately drawn
(a)Work out the size of angle a. Give a reason for your answer.(2)
(b)Work out the size of angle b. Give a reason for your answer.(2)
(Total for Question 6 is 4 marks)
7
The diagram shows two parallel lines crossed by a transversal. Two corresponding angles are marked (2x + 14) degrees and 74 degrees.
Diagram NOT accurately drawn
(a)Find the value of x.(2)
(b)Hence work out the size of the co-interior angle to the 74 degree angle.(1)
(Total for Question 7 is 3 marks)
8
AB and CD are parallel lines. P lies on AB and Q lies on CD. A straight line from Q also meets AB at point R, so that P, Q and R form a triangle, with points A, P and R lying in that order on line AB. Angle DQP = 122 degrees. Angle PRQ = 47 degrees.
Diagram NOT accurately drawn
(Total for Question 8 is 3 marks)
9
Angle ABE = (2x + 30) degrees and angle BCF = (3x - 10) degrees, where x = 32. Show that AB is parallel to CF.
Diagram NOT accurately drawn
(Total for Question 9 is 3 marks)
10
Lines l and m are parallel. A transversal crosses l at P and m at Q, and the angle between the transversal and l is 118 degrees. At Q, three further angles going all the way around the point are marked 90 degrees, 150 degrees and w, in addition to the angle co-interior to the 118 degree angle.
Diagram NOT accurately drawn
(Total for Question 10 is 3 marks)
11
The diagram shows two parallel lines cut by a transversal. At the intersection with line l, the four angles formed are labelled p, q, r, s (clockwise from top-left). At the intersection with line m, the four angles formed are labelled t, u, v, w (clockwise from top-left, in the same orientation).
A) r and v
B) s and t
C) r and t
D) p and r
(Total for Question 11 is 1 mark)
12
Lines l and m are parallel. Points P and R lie on l, and point Q lies on m, forming triangle PQR, with QP = QR. The angle between the transversal QP and line m, which is alternate to angle QPR, is marked 63 degrees.
Diagram NOT accurately drawn
(Total for Question 12 is 3 marks)
13
A car park has two straight rows of parking bays marked by parallel lines AB and CD. A diagonal walkway crosses AB at P and CD at Q. The angle between the walkway and AB, on the interior right of P, is 74 degrees.
Diagram NOT accurately drawn
(a)Work out the size of angle x. Give a reason for your answer.(2)
(b)Work out the size of angle y.(1)
(Total for Question 13 is 3 marks)
14
ABCD is a parallelogram, so AB is parallel to DC. The diagonal AC is drawn. Angle CAB = 38 degrees and angle ADC = 112 degrees.
Diagram NOT accurately drawn
(Total for Question 14 is 3 marks)
15
Lines l and m are parallel. A transversal crosses l at A, making an angle of 100 degrees with l, and meets m at point X. A second transversal crosses l at C and also meets m at X, making an angle of 55 degrees with m on the other side of X.
Diagram NOT accurately drawn
(Total for Question 15 is 3 marks)
16
The diagram shows two parallel lines cut by a transversal. Two co-interior (allied) angles are (4x - 5) degrees and (2x + 65) degrees.
Diagram NOT accurately drawn
(a)Form and solve an equation to find the value of x.(2)
(b)Hence work out the size of the smaller of the two angles.(1)
(Total for Question 16 is 3 marks)
17
The diagram shows two parallel lines cut by a transversal. Two alternate angles are marked (5x - 12) degrees and (3x + 20) degrees.
Diagram NOT accurately drawn
(a)Find the value of x.(2)
(b)Work out the size of the co-interior angle to the (5x - 12) degree angle.(2)
(Total for Question 17 is 4 marks)
18
Straight lines AB and CD are both crossed by a transversal PQ, meeting AB at E and CD at F. Angle AEP = (2x + 40) degrees and angle BEP = (3x + 10) degrees. Angle DFQ = (3x + 14) degrees, marked in the alternate position to angle AEP.
Diagram NOT accurately drawn
(a)Use angles on a straight line at E to find the value of x.(2)
(b)Hence show that AB is parallel to CD.(2)
(Total for Question 18 is 4 marks)
19
ABCD is a trapezium with AB parallel to DC. Angle DAB = (3x + 5) degrees and angle ADC = (2x + 25) degrees. Angle ABC = 95 degrees and angle BCD = y degrees.
Diagram NOT accurately drawn
(a)Use co-interior angles to find the value of x.(2)
(b)Work out the value of y.(2)
(Total for Question 19 is 4 marks)
20
Triangle ABC is isosceles with AB = AC, and BC lies along straight line m. A straight line l passes through A and is parallel to m. The angle between l and AB, on the left of A, is (4x + 10) degrees. Angle BAC (the apex of the triangle) is (2x + 20) degrees.
Diagram NOT accurately drawn
(a)Explain why angle ABC = (4x + 10) degrees.(1)
(b)Use angles on a straight line at A, together with the fact that triangle ABC is isosceles, to form and solve an equation for x.(2)
(c)Hence work out the size of angle ABC, marked y.(2)
(Total for Question 20 is 5 marks)
Mark scheme · 4.10 Angles in Parallel Lines
Question 1
B1 x = 72 (vertically opposite angles are equal)
Answer: x = 72 degrees
Question 2
B1 a = 62 cao
Answer: a = 62 degrees
Question 3
B1 b = 105 cao
B1 correct reason: corresponding angles are equal (oe, since l is parallel to m)
Answer: b = 105 degrees
Question 4
B1 x = 71 cao
B1 correct reason: alternate angles are equal (oe, l is parallel to m)
Answer: x = 71 degrees
Question 5
M1 180 - 109 oe
A1 y = 71 cao, with reason: co-interior (allied) angles sum to 180 degrees
Answer: y = 71 degrees
Question 6
(a) B1 a = 118 cao
(a) B1 correct reason: corresponding angles are equal (oe)
(a) Answer: a = 118 degrees
(b) M1 180 - 118 oe
(b) A1 b = 62 cao, with reason: co-interior angles sum to 180 degrees