Parallel lines
Find missing angles using the properties of parallel lines: corresponding angles are equal, alternate angles are equal, and co-interior angles are supplementary.
Worked examples
Finding a corresponding angle
Straightforward
Problem
Two parallel lines are cut by a transversal. One angle measures . Find the corresponding angle.
1
Recall the definition of corresponding angles.
Corresponding angles lie in matching positions at each parallel line — same side of the transversal, same location relative to the intersection.
2
State the relationship between corresponding angles.
When two parallel lines are cut by a transversal, corresponding angles are equal.
3
Write the answer.
Corresponding angle
Answer
Finding a co-interior angle
Moderate
Problem
Two parallel lines are cut by a transversal. One co-interior angle is . Find the other co-interior angle.
1
Recall where co-interior angles are located.
Co-interior angles lie between the parallel lines on the same side of the transversal.
2
State the relationship between co-interior angles.
Co-interior angles between parallel lines are supplementary — they add to .
3
Calculate the missing angle.
Answer
Solving for an unknown using co-interior angles
Challenging
Problem
Two parallel lines are cut by a transversal. The co-interior angles are and . Find the value of .
1
Write the equation using the co-interior angle relationship.
Co-interior angles are supplementary:
2
Collect like terms.
3
Solve for .
Answer
Practise
Q1·Straightforward
Two parallel lines are cut by a transversal. Which angles lie in matching positions at each parallel line — same side of the transversal, same location relative to the intersection?
Explanation
Corresponding angles are in matching positions at each parallel line — same side of the transversal and same location relative to the intersection. Between parallel lines, corresponding angles are equal.
Q2·Straightforward
Two parallel lines are cut by a transversal. The angles that lie between the parallel lines on opposite sides of the transversal are called ___.
Explanation
Alternate angles lie between the parallel lines on opposite sides of the transversal. They are equal when the lines are parallel.
Q3·Straightforward
Two parallel lines are cut by a transversal. One angle measures . Find the size of the corresponding angle in degrees.
Explanation
Corresponding angles between parallel lines are equal, so the corresponding angle is also .
Q4·Straightforward
Two parallel lines are cut by a transversal. One alternate angle measures . Find the other alternate angle in degrees.
Explanation
Alternate angles between parallel lines are equal, so the other alternate angle is also .
Q5·Moderate
Two parallel lines are cut by a transversal. One co-interior angle measures . Find the other co-interior angle in degrees.
Explanation
Co-interior angles (same-side interior angles) between parallel lines are supplementary: .
Q6·Moderate
In the diagram, . A transversal creates an angle of with line . Find the co-interior angle at line in degrees.
Explanation
Co-interior angles between parallel lines are supplementary: .
Q7·Moderate
Two parallel lines are cut by a transversal. The alternate angles are and . Find the value of .
Explanation
Alternate angles are equal: , so .
Q8·Moderate
Two parallel lines and are cut by a transversal. The transversal forms an angle of with . Find the supplement of the corresponding angle at in degrees.
Explanation
The corresponding angle at is (corresponding angles are equal). Its supplement is .
Q9·Challenging
Two parallel lines are cut by a transversal. The co-interior angles are and . Find the value of .
Explanation
Co-interior angles are supplementary: . Simplify: , so and .
Q10·Challenging
Two parallel lines are cut by a transversal. The alternate angles are and . Find the value of .
Explanation
Alternate angles are equal: . Subtract from both sides: . Add : , so .
Q11·Challenging
In triangle , and . A line is drawn through , parallel to . Find the angle this line makes with , measured between the parallel lines, in degrees.
Explanation
The line through is parallel to , and is a transversal. The angle at (between the parallel lines) and are alternate interior angles. Alternate angles are equal, so the angle is .
Q12·Challenging
Two parallel lines are cut by a transversal. An angle of is formed at the top parallel line. Find the angle that is supplementary to the alternate angle at the bottom parallel line.
Explanation
The alternate angle at the bottom parallel line equals (alternate angles are equal). The supplement of is .