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Angles and Parallel Lines

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Angles and Parallel Lines

Use the angle rules and descriptions of angle positions to solve each problem. Show working for calculations. Angles are measured in degrees.

Angle rules

When a transversal crosses parallel lines: corresponding angles are equal; alternate interior and alternate exterior angles are equal; co-interior angles sum to 180°. Vertically opposite angles are equal, and angles on a straight line sum to 180°.

1.A transversal crosses two parallel horizontal lines. At the upper intersection, angle 1 is in the upper-left position. At the lower intersection, angle 5 is also in the upper-left position. What is their relationship?

They are equal
They add to 180°
They add to 90°
They are always 45°

2.A transversal crosses two parallel horizontal lines. At the upper intersection, angles 1, 2, 3 and 4 are respectively in the upper-left, upper-right, lower-right and lower-left positions. At the lower intersection, angles 5, 6, 7 and 8 are in those same respective positions. Which pair are alternate interior angles?

Angles 3 and 6
Angles 1 and 5
Angles 2 and 6
Angles 4 and 8
Angles 3 and 5

3.A transversal crosses two parallel horizontal lines. At each intersection, angles 1, 2, 3 and 4 are respectively in the upper-left, upper-right, lower-right and lower-left positions; angles 5, 6, 7 and 8 occupy those same positions at the other intersection. If angle 2 is 68°, find angle 6 and name the rule you used.

4.A transversal crosses two parallel lines. A pair of co-interior angles on the same side of the transversal includes an angle of 117°. Calculate the other angle.

5.On a pair of parallel lines, one exterior angle is 124°. What is the alternate exterior angle? Explain briefly.

6.Two straight lines intersect. At the intersection, angle 1 is in the upper-left position, angle 2 in the upper-right, angle 3 in the lower-right and angle 4 in the lower-left. If angle 1 is 52°, find angles 2, 3 and 4. Give a rule for each value.

7.A transversal crosses two parallel lines, forming a pair of co-interior angles in the ratio 2:3. Find both angles. Show how you use their angle relationship.

8.A transversal crosses two parallel lines, forming corresponding angles of (3x + 12)° and (5x − 28)°. Find x and the size of each angle.

9.If a transversal crosses two lines and a pair of corresponding angles are equal, the two lines are parallel. State whether this is true or false and give the relevant reasoning.

TrueFalse

10.Explain how alternate interior angles differ from vertically opposite angles. Mention where each pair is found.

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