Two parallel lines are cut by a transversal. State whether corresponding angles are equal or supplementary.
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2
Two parallel lines are cut by a transversal. One angle is 84 degrees. State the size of the corresponding angle.
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3
Two parallel lines are cut by a transversal. One interior angle is 58 degrees. State the size of the alternate interior angle.
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4
Two parallel lines are cut by a transversal. One interior angle is 76 degrees. Find the co-interior (allied) angle on the same side of the transversal.
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5
State the name of the angle relationship: two angles are on the same side of the transversal, both inside the parallel lines, and they sum to 180 degrees.
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6
Two parallel lines are cut by a transversal. One angle at an intersection is 39 degrees. State the sizes of the other three angles at that same intersection.
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7
Two parallel lines are cut by a transversal. One interior angle is 47 degrees. State the alternate angle on the other parallel line.
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8
A transversal cuts two parallel lines. At one intersection the four angles, in order around the point, are 63 degrees, x, y and z. Find x, y and z.
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9
Two parallel lines are cut by a transversal. At the first intersection an obtuse angle is 133 degrees. State the size of the angle that is co-interior with it at the second intersection.
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10
Lines l and m are parallel. A transversal cuts them and creates an angle of 52 degrees inside at the first intersection, on the left of the transversal. Find the alternate interior angle at the second intersection.
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11
A transversal meets two parallel lines. At the first intersection two adjacent angles are 71 degrees and y degrees, forming a straight line. Find y.
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12
Two parallel lines are cut by a transversal. One angle is labelled 61 degrees. A different angle at the same intersection, vertically opposite to it, is labelled z. Find z.
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13
A transversal intersects two parallel lines. At one intersection an angle is 88 degrees. At the other intersection, the corresponding angle is labelled w. The angle adjacent to w on a straight line is labelled v. Find w and v.
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14
Two parallel lines are cut by a transversal. At the top intersection the angles are a and b, where a and b lie on a straight line together and b = 2a. The angle c at the bottom intersection is co-interior with a. Find a, b and c.
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15
A transversal cuts two parallel lines. At one intersection, an angle next to the transversal is 3x degrees. The co-interior angle at the other intersection is (x + 60) degrees. Find x.
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16
Two parallel lines are cut by a transversal. At one intersection, two angles on the same straight line are 3x degrees and 2x degrees. Find x, and hence find the size of the angle that is corresponding to the 3x angle at the other intersection.
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17
A transversal cuts two parallel lines. At one intersection an angle adjacent to the transversal is 46 degrees. At the second intersection, the alternate angle is labelled p and the angle co-interior to the 46 degree angle (at the second intersection) is labelled q. Find p and q.
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18
A ramp is built so that its sloped surface is parallel to a horizontal guide rail. A support strut crosses both, acting as a transversal. The strut makes an angle of (4x - 15) degrees with the ramp surface and an angle of (2x + 25) degrees with the guide rail, measured as alternate angles. Find x.
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19
Stretch question. A transversal cuts two parallel lines. At the first intersection, angle a is co-interior with angle e at the second intersection, where e = 118 degrees. At the first intersection, angles a and b lie on a straight line together, and angles b and d are vertically opposite. Find a, b and d.
(4)
Mark scheme · KS3.M-G9D Angles in Parallel Lines: Fluency and Exam Drill
Question 1
B1 equal
Answer: Equal
Question 2
B1 84 degrees cao
Answer: 84 degrees
Question 3
B1 58 degrees cao
Answer: 58 degrees
Question 4
M1 uses co-interior angles sum to 180
A1 104 degrees cao
Answer: 104 degrees
Question 5
B1 co-interior (allied) angles
Answer: Co-interior (allied) angles
Question 6
M1 uses angles on a straight line sum to 180 to find 141 degrees
A1 the other three angles are 141, 39 and 141 degrees cao
Answer: 141 degrees, 39 degrees, 141 degrees
Question 7
B1 47 degrees cao
Answer: 47 degrees
Question 8
M1 uses angles on a straight line sum to 180 to find 117 degrees
A1 x = 117, y = 63, z = 117 degrees cao
Answer: x = 117, y = 63, z = 117 degrees
Question 9
M1 uses co-interior angles sum to 180
A1 47 degrees cao
Answer: 47 degrees
Question 10
M1 uses alternate angles are equal
A1 52 degrees cao
Answer: 52 degrees
Question 11
M1 uses angles on a straight line sum to 180
A1 y = 109 degrees cao
Answer: 109 degrees
Question 12
M1 uses vertically opposite angles are equal
A1 z = 61 degrees cao
Answer: 61 degrees
Question 13
M1 uses corresponding angles are equal so w = 88 degrees
A1 v = 92 degrees cao
Answer: w = 88 degrees, v = 92 degrees
Question 14
M1 forms a + 2a = 180
A1 a = 60 degrees, b = 120 degrees cao
A1 c = 120 degrees (co-interior with a) cao
Answer: a = 60, b = 120, c = 120 degrees
Question 15
M1 uses co-interior angles sum to 180: 3x + (x+60) = 180
M1 simplifies to 4x + 60 = 180
A1 x = 30 cao
Answer: 30
Question 16
M1 uses 3x + 2x = 180
A1 x = 36, so the 3x angle = 108 degrees
A1 corresponding angle = 108 degrees cao
Answer: x = 36; corresponding angle = 108 degrees
Question 17
M1 uses alternate angles are equal: p = 46 degrees