ACT Preparation / Unit 13 ACT 1206 worked example, 60 to 90 seconds
Finding Angles Through Parallel Lines
The idea
An angle problem with parallel lines is solved in three steps. First, mark the parallel lines and the transversal, and label the given angle. Second, move from angle to angle one fact at a time: vertical angles are equal, alternate interior and corresponding angles are equal, and angles on a straight line or same-side interior angles add to 180°. Third, name the fact used at each step, so that each move can be checked.
In practice
Worked example: parallel lines are crossed by a transversal. One angle at the upper crossing is 3x + 10, and its corresponding angle at the lower crossing is 5x − 30. Corresponding angles are equal, so 3x + 10 = 5x − 30, giving x = 20 and an angle of 70°. The angle beside it on the line is 180 − 70 = 110°.
Where people slip
An equation built from two angles needs the right relationship. If the angles were same-side interior, the equation would be (3x + 10) + (5x − 30) = 180 instead, with x = 25.
Your place on the trail
Every lesson rests on earlier ones and opens later ones. Tap any to jump.
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