Alternate, corresponding and co-interior angles.
17 original questions, 63 marks. Print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.
AB and CD are parallel straight lines.
A straight line crosses AB at E and crosses CD at F. On line AB, A is to the left of E and B is to the right of E. On line CD, C is to the left of F and D is to the right of F.
Angle AEF = 62°.
Work out the size of angle CFE.
Give a reason for each stage of your working.
Two straight lines are parallel. A third line crosses them. Two angles lie between the parallel lines, on opposite sides of the crossing line, in a Z shape. One of these angles is 72°.
Write down the size of the other angle and the name of this type of angle.
Two straight lines are parallel. A third line crosses them. Two angles are in matching positions, one at each crossing, in an F shape. One of these angles is 115°.
Write down the size of the other angle and the name of this type of angle.
PQ and RS are parallel straight lines.
A straight line crosses PQ at E and crosses RS at F. On line PQ, P is to the left of E and Q is to the right of E. On line RS, R is to the left of F and S is to the right of F.
Angle QEF = 74°.
Two straight lines are parallel. A third line crosses them. Two angles lie between the parallel lines, on the same side of the crossing line, in a C shape. One of these angles is 108°.
Work out the size of the other angle. Give the name of this type of angle.
Two straight lines are parallel and are crossed by a third line. Write down the name of each pair of angles, and say what you know about their sizes.
AB and CD are parallel straight lines.
A straight line GEFH crosses AB at E and crosses CD at F, where G is above the line AB and H is below the line CD. On line AB, A is to the left of E and B is to the right of E. On line CD, C is to the left of F and D is to the right of F.
Angle GEB = 63°.
Two straight lines are parallel and are crossed by a third line. Two alternate angles are (3x + 10)° and (5x − 30)°.
Work out the value of x.
Two straight lines are parallel and are crossed by a third line. Two corresponding angles are (4x − 12)° and (x + 30)°.
Work out the value of x, and the size of each angle.
DE and FG are parallel straight lines.
Triangle ABC is drawn so that A lies on DE, and B and C both lie on FG.
D is to the left of A and E is to the right of A.
Angle DAB = 48° and angle ACB = 63°.
Work out the size of angle BAC.
Give a reason for each stage of your working.
Two straight lines are parallel and are crossed by a third line. Two co-interior angles are (2x + 15)° and (3x − 5)°.
Work out the value of x, and the size of the larger angle.
A straight line crosses line AB at the point P and crosses line CD at the point Q, where P is above Q. On line AB, B is to the right of P. On line CD, D is to the right of Q.
Angle QPB, between PQ and PB and inside the region between the two lines, is 104°.
Angle PQD, between QP and QD and inside the region between the two lines, is 76°.
Show that AB is parallel to CD.
Give reasons for your answer.
AB and CD are parallel straight lines.
E lies on AB. F and G both lie on CD, with F to the left of G.
A is to the left of E and B is to the right of E.
EF = EG and angle AEF = 64°.
Work out the size of angle FEG.
Give a reason for each stage of your working.
ABCD is a trapezium in which AB is parallel to DC.
The diagonal BD is drawn.
Angle DAB = 74° and angle ADB = 68°.
AB and CD are parallel straight lines.
E lies on AB. F and G both lie on CD, with F to the left of G.
A is to the left of E and B is to the right of E.
Angle AEF = 67° and angle BEG = 67°.
Show that triangle EFG is an isosceles triangle.
Give a reason for each stage of your working.
AB and CD are parallel straight lines. A straight line crosses them both.
Two co-interior angles between the parallel lines are (3x + 20)° and (2x − 15)°.
Work out the size of the smaller of these two angles.
You must show all your working.
AB and CD are parallel straight lines, with AB above CD.
E lies on AB and G lies on CD. F is a point between the two lines, to the right of both E and G, so that EFG forms a zigzag.
Angle BEF = 38° and angle DGF = 44°, where B is to the right of E and D is to the right of G.
Work out the size of angle EFG.
Give a reason for each stage of your working.
Every question here is original and written by Robinson Tuition. The grade follows the Edexcel grade descriptors and suits AQA and OCR too; this is not an exam-board paper.