Find the missing angle in a pair of parallel lines

Key takeaway: When two lines are parallel, the angle relationship usually comes from corresponding, alternate interior, or supplementary angles. The key is to track which angle in the diagram matches α, then use the given measure to compare them.

Step 1: Use the parallel lines rule

Because $a \parallel b$, angles formed by a transversal have fixed relationships.

Step 2: Match the angle to the diagram

Look for the angle that is equal to, or supplementary to, the given angle in the figure. In these problems, the marked angle usually sits in a corresponding or alternate interior position.

Step 3: Read off the value of $\alpha$

From the diagram, $\alpha = 25^\circ$.

Final answer

$\alpha = 25^\circ$

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Pitfalls the pros know 👇 A common mistake is to add angles that should actually be equal. With parallel lines, many angles are the same size, so first check whether the pair is corresponding or alternate interior before using a sum.

What if the problem changes? If the given angle were placed on the other side of the transversal, you might need to use the supplementary angle instead. Then the answer would be found by subtracting from $180^\circ$ rather than copying the same value.

Tags: parallel lines, corresponding angles, alternate interior angles