The worksheets themselves are in German – just as in class. The editor is only available in German so far.
Angle rules – worksheets to print
Work out missing angles: the angle sum in triangles and quadrilaterals, adjacent and vertically opposite angles, corresponding and alternate angles at parallel lines and the exterior angle of a triangle – each with a sketch.
- Choose the number of tasks and the difficulty yourself
- With an answer sheet and, if you like, a QR code to the answers
- At three levels (★ to ★★★) and as group A and B
- As a single worksheet or as a task on a mixed worksheet
Angle rules: explained simply
You work out missing angles in a sketch. You only need a few fixed rules for it, for example the angle sum in a triangle.
How to work it out
- The angles in a triangle add up to 180°, the angles in a quadrilateral to 360°.
- Adjacent angles on a line add up to 180°, vertically opposite angles are equal. At parallel lines, corresponding angles and alternate angles are equal.
An example, step by step
In a triangle α = 52° and β = 67°. How big is γ?
- The three angles add up to 180°.
- Work out 52° + 67° = 119°.
- γ = 180° − 119° = 61°. Check: 52° + 67° + 61° = 180°.
Understand other variations
Parallel lines
When a line crosses two parallel lines, corresponding angles are equal (both at the same place of the crossing). Alternate angles lie on different sides of the crossing line and are equal as well. If one angle is 70°, its adjacent angle is 110°.
Exterior angle
The exterior angle of a triangle equals the two interior angles that are not next to it, added together. For α = 50° and β = 60° the exterior angle at γ is 110°.
Your turn
In an isosceles triangle the angle at the apex is 40°. How big are the base angles?
Show the answer and method
(180° − 40°) : 2 = 70°. Check: 70° + 70° + 40° = 180°.
Ready-made worksheets: Angle rules
Click the picture to see the worksheet large and print it. “Use” opens it in the editor.