Angles in a quadrilateral

A complete lesson on the interior angle sum of a quadrilateral. Requires pupils to know the interior angle sum of a triangle, and also know the angle properties of different quadrilaterals.

Activities included:

Starter:
A few simple questions checking pupils can find missing angles in triangles.

Main:

• A nice animation showing a smiley moving around the perimeter of a quadrilateral, turning through the interior angles until it gets back to where it started. It completes a full turn and so demonstrates the rule. This is followed up by instructions for pupils to try the same on a quadrilateral that they draw.
• Instructions for pupils to use their quadrilateral to do the more common method of marking the corners, cutting them out and arranging them to form a full turn. This is also animated nicely.
• Three example-problem pairs where pupils find missing angles.
• Three worksheets, with a progression in difficulty, for pupils to work through. The first has standard ‘find the missing angle’ questions. The second asks pupils to find missing angles, but then identify the quadrilateral according to its angle properties. The third is on a similar theme, but slightly harder (eg having been told a shape is a kite, work out the remaining angles given two of the angles).
• A nice extension task, where pupils are given two angles each in three quadrilateral and work out what shapes they could possibly be.

Plenary:

• A look at a proof of the rule, by splitting quadrilaterals into two triangles.
• A prompt to consider what the sum of interior angles of a pentagon might be.

Printable worksheets and answers included throughout.

Please review if you buy as any feedback is appreciated!