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Angles in Parallel Lines

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Angles in Parallel Lines

Use this angle labelling throughout: at the upper crossing, angles 1, 2, 3 and 4 are upper-left, upper-right, lower-right and lower-left, respectively. At the lower crossing, angles 5, 6, 7 and 8 are upper-left, upper-right, lower-right and lower-left, respectively. The transversal crosses two parallel lines. Use the angle relationships to identify pairs and calculate missing angles.

Spot the angle relationships

Use the angle positions described in the instructions. Corresponding angles are equal, alternate interior angles are equal, and co-interior angles add to 180°.

1.Which pair is alternate interior: (A) angles 1 and 5, (B) angles 3 and 5, (C) angles 2 and 6, or (D) angles 4 and 8?
  • A. Angles 1 and 5
  • B. Angles 3 and 5
  • C. Angles 2 and 6
  • D. Angles 4 and 8
2.Using the angle positions described in the instructions, write the angle corresponding to angle 2.
3.Angles 4 and 5 lie between the parallel lines on the same side of the transversal. What is the special name for this pair?
4.True or false? Angles 3 and 5 are equal because they are alternate interior angles.
TrueFalse

Solve the missing angles

Show your reasoning. A straight line makes 180°, and vertically opposite angles are equal. Use the angle positions described in the instructions when a question refers to numbered angles.

5.A road crosses two parallel cycle paths. If angle 1 is 68°, find angle 5. Angles 1 and 5 are in corresponding positions.
6.At the two crossings of a transversal and parallel lines, angle 3 and angle 5 are alternate interior angles. If angle 3 is 124°, find angle 5.
7.Angle 4 is 73°. Angles 4 and 5 are co-interior. Calculate angle 5.
8.At one crossing of the two parallel lines, an angle is 116°. What is the size of the adjacent angle on the same straight line?
9.A student says, “If angle 2 is 105°, angle 8 must also be 105° because they are vertically opposite.” Is the student correct? Explain using the angle positions described in the instructions.
10.A pair of corresponding angles is labelled (3x + 15)° and (5x − 25)°. Find x and the size of each angle.

2 printable pages

  • Angles in Parallel Lines, page 1 of 2: Spot the angle relationships

    Page 1

  • Angles in Parallel Lines, page 2 of 2: Solve the missing angles

    Page 2

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