Reasoning about angles in polygons | Maths | Quizalize & Oak National Academy

Starter quiz

Look at the hands on this clock face and the arrow. The angle formed is __________.
- acute
- obtuse
- obtuse
- reflex ✓
Where two lines create an angle within a shape, we call this part a ______.
- 'vertex' ✓
The angles in a triangle sum to ___.
- 90°
- 180° ✓
- 270°
- 360°
The angles in a quadrilateral sum to ___.
- 90°
- 180°
- 270°
- 360° ✓
Fill in the missing product 3 × 180 = ______
- '540' ✓
The triangle is not to scale. The missing angle labelled m is ______°
- '110' ✓

Exit quiz

What do these lines represent on two sides of this polygon?
- The length of both lines are the same. ✓
- The markers divide each line into two parts.
- The length of both lines are different.
Any polygon can be always be divided into what other type of polygon?
- Circles
- Rectangles
- Triangles ✓
- Squares
You can work out the sum of the angles in a polygon by:
- Multiplying the number of angles by 180
- Multiplying the number of internal triangles by 180 ✓
- Dividing 180 by the number of angles.
The size of missing angle a is ______ degrees.
- '108' ✓
A triangle is placed inside a rectangle. Tick the calculation that helps to find missing angle b.
- 180° − 46°
- (180° − 46°) ÷ 2 ✓
- 180° ÷ 2 − 46°
A triangle is placed inside a rectangle. The size of missing angle c is ______ degrees.
- '23' ✓

Worksheet

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Presentation

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Lesson Details

Key learning points

Angles describe and measure a turn or rotation.
Protractors can be used to measure and draw angles.
Use knowledge of right angles to estimate and compare angles.

Common misconception

Pupils think that composing larger polygons of smaller triangles that are not formed as a result of drawing a line from one vertex to another will help them to identify the sum of the angles.

Highlight how the formation of triangles within a polygon must be from vertex to vertex and demonstrate how the angles of each triangle where they meet sum to the internal angle of the polygon.

Keywords

Angle - An angle is a measure of turn.
Sum - The sum is the result of adding two or more numbers.
Vertex - A vertex is a point where two or more lines meet.
Polygon - A polygon is a 2D shape made up of three or more straight lines.