Angles in parallel linesAlternate angles
Name: Date:
The two lines are parallel. Find x.
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Alternate angles worksheets
Alternate angles sit on opposite sides of the crossing line, between the two parallels, and they are equal. These free printable worksheets draw the figure, mark one, and ask for the other.
Kid stuck on one? You don’t just get the sheet.
Alternate angles
The answer key prints on a separate page.
What's on this sheet
The letter Z is the picture here, and the two angles are tucked into its corners. They are on opposite sides of the transversal and both inside the parallel pair, which is what "alternate" and "interior" mean before either word is used. Finding the Z is the whole method.
Why this sheet works
It is worth knowing that this rule is not separate from corresponding angles. An alternate pair is a corresponding pair with one of them swapped for the angle opposite it across the crossing, and those two are equal too. A child who sees the connection has two rules resting on one fact rather than two facts to keep apart.
How this one works
One question from this sheet, worked through a step at a time.
55° and x
55°andx
alternateangles
55°=x
x=55°
- Start with the arrows: they say the two lines are parallel. Without that, none of the angle facts apply and this picture would not have an answer.
- Now find where the two marked angles sit. They are between the two parallel lines, on opposite sides of the slanted one. That makes them alternate angles.
- Alternate angles are equal, so x is the same as the angle already marked. x = 55°. Nothing to work out — but only once you have seen which pair it is.