Angles in Parallel Lines - Worksheets, Questions and Revision

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KS3 · Geometry and Measures

KS3.M-G9 Angles in Parallel Lines

AQA KS3.M-G9 · Calculators not allowed · about 60 minutes
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
Two parallel lines are cut by a transversal. State whether alternate interior angles are equal, add to 180 degrees, or are complementary.
(1)
2
In the diagram two parallel lines l and m are cut by a transversal. Angle a on line l is 64 degrees as shown where a and b are alternate interior angles. Work out angle b.
Figure (to be drawn): Lines l and m are parallel. Transversal crosses them. Angle a (interior) = 64 degrees on upper intersection. Angle b is the alternate interior angle at lower intersection.
(2)
3
Lines p and q are parallel. A transversal meets them. Angle x and angle y are corresponding angles. If x = 118 degrees, find y.
Figure (to be drawn): Parallel lines p and q with a transversal. x is the exterior angle on the top left at the first intersection = 118. y is the corresponding angle at the second intersection.
(2)
4
On parallel lines r and s a transversal makes two interior angles on the same side of the transversal measured as 50 degrees and z degrees. These are co-interior angles. Work out z.
Figure (to be drawn): Parallel lines r and s, transversal; interior angles on same side are 50 degrees and z.
(2)
5
A pair of parallel lines is cut by a transversal. At the first (upper) intersection, the interior angle below the line, on the right of the transversal, is 42 degrees. At the second (lower) intersection, angle a is the interior angle, between the two parallel lines, on the same right-hand side of the transversal (the co-interior / allied angle to the 42-degree angle). Find a and give a short reason.
Figure (to be drawn): Two parallel lines with transversal. At the first (upper) intersection, the angle marked 42 degrees is below the line, on the right of the transversal, i.e. between the two parallel lines (interior). At the second (lower) intersection, angle a is below the transversal's crossing but above the lower line, i.e. between the two parallel lines, on the same (right) side of the transversal as the 42-degree angle - the co-interior angle to it.
(3)
6
State the name of the angle relationship: two angles are on the same side of the transversal inside the parallel lines and add to 180 degrees.
(1)
7
Two parallel lines are cut by a transversal. One interior angle is 73 degrees. Find the four angles at that intersection and state briefly why each equals or supplements 73 where appropriate.
Figure (to be drawn): At one intersection angles are labelled; one interior angle = 73. The other three at same point are requested.
(2)
8
In the diagram lines a and b are parallel. At the first intersection an acute angle is 35 degrees. At the second intersection on the same side of the transversal the angle is labelled c and is interior. At the corresponding position on the second intersection the exterior angle is d. Find c and d.
Figure (to be drawn): Parallel lines a and b with transversal. First intersection acute interior angle = 35. At second intersection interior angle on same side labelled c; exterior corresponding angle labelled d.
(3)
9
Two parallel lines are cut by a transversal. At the first intersection an obtuse angle is 122 degrees. At the second intersection the angle in the corresponding position is labelled e. Find e and give the reason.
Figure (to be drawn): Parallel lines with transversal; first intersection obtuse angle = 122; corresponding angle at second intersection labelled e.
(2)
10
A transversal cuts two parallel lines. At one intersection the four angles are 48, x, y and z in order around the point. Given one is 48, find x, y and z and give a one-line reason for each.
Figure (to be drawn): Four angles around an intersection: one is 48, others labelled x, y, z
(2)
11
Lines l and m are parallel. A transversal cuts them and creates an angle of 29 degrees inside at the top left of the first intersection. Find the angle vertically opposite to the corresponding angle at the second intersection that matches the 29 degree angle. Explain your steps.
Figure (to be drawn): Parallel lines l and m, transversal. Angle at first intersection top left = 29; consider corresponding and vertically opposite at second intersection.
(3)
12
A transversal meets two parallel lines. At the first intersection two adjacent angles are 67 degrees and t degrees. On the same side of the transversal at the second intersection the interior angle is u degrees and is co-interior with t. Find t and u.
Figure (to be drawn): First intersection adjacent angles 67 and t; t is interior. At second intersection u is co-interior with t.
(2)
13
Two parallel lines are cut by a transversal. One angle is labelled 54 degrees. A different angle at the lower intersection is labelled v and is alternate exterior to the 54 degree angle. Find v and state the property used.
Figure (to be drawn): Parallel lines and transversal; given angle 54, angle v is alternate exterior at other intersection.
(3)
14
A transversal intersects two parallel lines. At one intersection an angle is 96 degrees. At the other intersection, the angle adjacent to the corresponding angle is w. Find w.
Figure (to be drawn): Parallel lines and transversal; one intersection angle = 96; at second intersection the corresponding angle is 96 and adjacent to it is w.
(2)
15
Two parallel lines are cut by a transversal. Angles at one intersection are labelled 2x and 3x where they are adjacent. Find x and the four angles at that intersection.
Figure (to be drawn): At one intersection adjacent angles are 2x and 3x; they share a straight line.
(3)
16
A transversal cuts two parallel lines. At one intersection an angle next to the transversal is 41 degrees. At the other intersection the corresponding angle is p and the interior on the same side is q. Find p and q.
Figure (to be drawn): Parallel lines and transversal; given angle 41 near transversal at first intersection; at second intersection corresponding angle p, co-interior q.
(2)
17
Stretch: Two parallel lines are cut by a transversal. At the top intersection the angles are a and b with a = 3b. At the bottom intersection the angle corresponding to a is 50 degrees. Find a and b, showing your steps.
Figure (to be drawn): Top intersection angles a and b are adjacent, with a = 3b. Corresponding angle to a at bottom intersection = 50 degrees.
(4)
18
Stretch: A transversal cuts two parallel lines. At one intersection the angles are labelled in order around the point as 6y, z, (2y + 10) and w. Given z is vertically opposite to 6y and w is supplementary to (2y + 10), find y, z and w.
Figure (to be drawn): Four angles around an intersection labelled 6y, z, (2y + 10), w in clockwise order. z vertically opposite 6y; w supplementary to (2y + 10).
(5)
Mark scheme · KS3.M-G9 Angles in Parallel Lines

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Question 2

Question 3

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Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18