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Alternate angles, step by step

Alternate angles sit on opposite sides of the crossing line, between the two parallels, and they are equal.

Practice Practice sheetNew questions
The question
40°x

40° and x

40°andx
alternateangles
40°=x
x=40°
  1. 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.
  2. 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.
  3. Alternate angles are equal, so x is the same as the angle already marked. x = 40°. Nothing to work out — but only once you have seen which pair it is.

How it works.

  1. 01

    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.

  2. 02

    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.

  3. 03

    Alternate angles are equal, so x is the same as the angle already marked. x = 40°. Nothing to work out — but only once you have seen which pair it is.

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