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Angles and Parallel Lines
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Angles and Parallel Lines
A road planner is checking where a straight road crosses two parallel streets. Use the angle rules to work out the missing angles. Show your calculations where asked.
Know the angle rules
When a transversal crosses parallel lines, compare the positions of the angles and use the relationships between them. Also remember that vertically opposite angles are equal, and angles on a straight line add to 180°.
1.Match each angle relationship to its rule.
- Corresponding angles
- Alternate interior angles
- Co-interior angles
- Equal
- Equal
- Add to 180°
2.Two parallel streets are crossed by a straight road. One angle is 68°. What is the size of the corresponding angle?
- 22°
- 68°
- 112°
- 180°
3.An alternate interior angle is 124°. What is the size of the other angle in the pair?
4.Two co-interior angles are 73° and x°. Find x.
5.Which statement is false when a transversal crosses two parallel lines?
- Corresponding angles are equal.
- Co-interior angles add to 180°.
- Alternate interior angles are equal.
- Every angle formed is equal to every other angle.
6.A transversal crosses two parallel lines. One of the angles is 56°. What are the sizes of the other seven angles? Group equal angles together.
7.Two co-interior angles are (3x + 15)° and (2x + 40)°. Find x, then calculate both angles.
8.One angle at an intersection is 131°. Find the acute angle next to it on the same straight line.
9.Complete the sentence: Co-interior angles on the same side of a transversal add up to degrees.
10.Alfie says, “If one angle made by a transversal is 72°, all eight angles must be 72°.” Explain why Alfie is mistaken, and give the two angle sizes that actually appear.
11.Draw two parallel lines crossed by a transversal. Mark one pair of corresponding angles, one pair of alternate interior angles, and one pair of co-interior angles. Label each pair clearly.
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