Practice Maths

Topic Review — Angles

Mixed Practice — L58 – L60

This review covers all lessons in the Angles topic: parallel lines, corresponding and alternate angles, and co-interior angles. Try each question before checking your answers.

Review Questions

  1. Angle Foundations Fluency

    1. Two angles on a straight line are 63° and x. Find x.
    2. Three angles at a point are 140°, 95°, and x. Find x.
    3. Two parallel lines are cut by a transversal. One angle is 78°. List all 8 angles formed (there will be two different values).
    4. A transversal makes a 90° angle with a pair of parallel lines. What are all 8 angles?
    5. True or False: Vertically opposite angles are supplementary.

  2. Corresponding and Alternate Angles Fluency

    1. Find the corresponding angle to 83° when lines are parallel.
    2. Find the alternate angle to 119° when lines are parallel.
    3. Find the corresponding angle to 47°.
    4. Find the alternate angle to 63°.
    5. Which letter shape helps you identify corresponding angles? Which helps with alternate angles?
    6. Are corresponding angles on the same side or opposite sides of the transversal?

  3. Co-interior Angles Fluency

    1. Two parallel lines are cut by a transversal. One co-interior angle is 68°. Find the other.
    2. One co-interior angle is 115°. Find the other.
    3. One co-interior angle is 90°. Find the other.
    4. True or False: Co-interior angles are always equal.
    5. What letter shape is associated with co-interior angles?

  4. Identify and Calculate Understanding

    Two parallel lines are cut by a transversal. For each description, name the angle relationship and find the unknown angle.

    1. Angles at the same corner of each intersection: given 56°.
    2. Angles on the same side between the parallel lines: given 74°.
    3. Angles on opposite sides between the parallel lines: given 101°.
    4. An angle (4x + 5)° is a co-interior angle with 79°. Find x.
    5. An angle (2x − 8)° is a corresponding angle with 64°. Find x.
    6. An angle (3x + 15)° is an alternate angle with 90°. Find x.

  5. Reasoning and Real-World Problems Problem Solving

    1. Two lines are cut by a transversal. A pair of co-interior angles measures 88° and 87°. Are the lines parallel? Justify your answer.
    2. A pair of alternate angles measures 53° each. Are the lines parallel? Justify your answer.
    3. A road crosses two parallel fences at an angle of 58°. At the second fence, a worker measures a co-interior angle. What should the measurement be?
    4. A staircase railing runs parallel to the stairs. A vertical support post cuts across both. If the post makes a 72° angle with the stairs, what angle does it make with the railing at the corresponding position? At the co-interior position?
    5. In a diagram, angle A and angle B are co-interior. Angle A = (6x − 10)° and angle B = (2x + 30)°. Find x, then find both angles. Verify your answers sum to 180°.

  6. Angle Relationships Summary Understanding

    1. Complete the table:
      Angle PairShape to look forRelationship (equal or sum to 180°)
      Corresponding??
      Alternate??
      Co-interior??
    2. Explain in your own words how to determine whether two lines are parallel using angle measurements.

  7. Angle types: Fluency

    1. An angle is formed by two parallel lines and a transversal. One angle at the first line is 55°. Find all other angles at both intersections, naming the relationship you used.
    2. Two angles are co-interior. One is (3x + 10)° and the other is (5x − 30)°. Are the lines parallel? Check by finding x and verifying.

  8. Vertically opposite and adjacent angles: Fluency

    1. Two lines intersect, forming angles of 42°, p, 42°, and q. Find p and q.
    2. An angle is 3 times its supplementary angle. Find both angles.
    3. An angle is 20° more than its complement. Find both angles.
    4. Define “supplementary” and “complementary” angles and give an example of each.

  9. Angles and triangles: Understanding

    1. A transversal crosses two parallel lines. One of the angles formed is 65°. Without measuring, list all 8 angles and identify which are equal and which are supplementary.
    2. The exterior angle of a triangle is 115°. One of the non-adjacent interior angles is 48°. Find the other non-adjacent interior angle.

  10. Prove lines are parallel: Problem Solving

    1. Two lines are cut by a transversal. The co-interior angles are 92° and 88°. Are the lines parallel? Justify your answer.
    2. Corresponding angles are 73° and 73°. Are the lines parallel? Which law of parallel lines are you using?
    3. Alternate angles are 61° and 59°. Are the lines parallel? Explain why or why not.
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