Math PicnicFree printable practice

Angles on a line and around a point worksheets

Angles that sit side by side share what is left of the whole: on a straight line they fill 180°, around a point a full 360°. These free printable worksheets draw three angles meeting at a vertex and mark one with x.

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Angles on a line and around a point
Angles on a line and around a point worksheet — Three angles, 180° or 360°, free printable with answer key

The answer key prints on a separate page.

What's on this sheet

This is the multi-step case the angle-pair sheets leave out. A pair of angles fills a right angle or a straight line; here three share the vertex, so the missing one is the whole minus the two that are given. Add the known angles first — that is the step a child skips — then take the sum from 180 or 360.

Why this sheet works

Which whole applies is the reading the figure asks for. Three angles opening off a straight line add to 180; three fanning all the way around a point add to 360, and a child who reaches for the wrong total gets a plausible wrong answer. The instruction names the total and the picture shows it, so the choice is made from the figure rather than guessed.

How this one works

One question from this sheet, worked through a step at a time.

Angles on a line: 50°, x, 40°

50° + 40° + x=180°
50° + 40°=90°
180° − 90°=90°
  1. The angles on a straight line add up to 180°, so all three together make 180°.
  2. Add the two you are given first: 50 + 40 = 90.
  3. Then take that from 180°: 180 − 90 = 90. So x = 90°.

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