Angles in Parallel Lines

When a straight line crosses two parallel lines, some angles are linked by angle facts. Corresponding angles are equal, alternate angles are equal, and co-interior angles add to 180°. First identify the angle relationship, then use the correct fact to find the missing angle.

Common mistake: Do not treat all angles in parallel lines as equal. Co-interior angles add to 180°, so if one is 110°, the other is 70°.

Summary diagrams showing alternate angles, corresponding angles, vertically opposite angles, and co-interior angles in parallel lines
Worked example:
Work out the size of the angle marked \(x\)
Parallel lines cut by a transversal with a 62° corresponding angle and angle x.
  1. Step 1
    The two marked angles are corresponding angles.
  2. Step 2
    Corresponding angles on parallel lines are equal.
    \[x = 62\]
Answer:
\[x = 62^\circ\]
Worked example:
Work out the sizes of the angles marked \(x\) and \(y\), in degrees
Parallel lines and a triangle with a 62° corresponding angle, a 43° base angle and unknown angles x and y
  1. Step 1
    First find x using corresponding angles on the parallel lines.
    \[x = 62^\circ\]
  2. Step 2
    Then use the three angles in the triangle, which add to 180°.
    \[y = 180 - 62 - 43 = 75^\circ\]
Answer:
\[x = 62^\circ,\quad y = 75^\circ\]
Start quiz →
We use optional Google Analytics cookies to understand site traffic. They stay off unless you accept.