New
New
Year 8

# Problem solving with polygons

I can use my knowledge of polygons to solve problems.

New
New
Year 8

# Problem solving with polygons

I can use my knowledge of polygons to solve problems.

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## Lesson details

### Key learning points

1. Problems can be solved using parallel line angle facts.
2. Problems can be solved using interior and exterior angles of polygons.
3. Problems can be solved and the solution justified using angle facts.
4. It is possible to write algebraic statements about connected angles.
5. Your knowledge of algebraic manipulation may be useful.

### Common misconception

Pupils might not know how to start an angle problem if they focus too much on the final solution.

You can start an angle problem by working out any angle on the diagram. The more angles you work out, the easier the final solution becomes.

### Keywords

• Corresponding angles - Corresponding angles are a pair of angles at different vertices on the same side of a transversal in equivalent positions.

• Alternate angles - A pair of angles both between or both outside two line segments that are on opposite sides of the transversal that cuts them.

• Co-interior angles - Co-interior angles are on the same side of the transversal line and in between the two other lines.

• Interior angles - An interior angle is an angle formed inside a polygon by two of its edges.

• Exterior angles - An exterior angle is an angle on the outside of a polygon between an extension of an edge and its adjacent edge.

### Licence

This content is © Oak National Academy Limited (2023), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

## Starter quiz

### 6 Questions

Q1.
Match each pair of angles with the keywords that describe the relationship between them.

corresponding angles

co-interior angles

alternate angles

Correct Answer:∠HEC and ∠GEF,vertically opposite angles

vertically opposite angles

Q2.
A dodecagon has 12 sides. Find the sum of the interior angles in a dodecagon.
180°
360°
2160°
2520°
Q3.
Exterior angles for any polygon sum to °.
Correct Answer: 360, three hundred and sixty, 360°
Q4.
Each exterior angle for a regular hexagon is °.
Q5.
Each interior angle in a regular octagon is °.
Correct Answer: 135, one hundred and thirty five, 135°
Q6.
The pentagon and hexagon in the diagram are both regular. The angle marked in the diagram is °.
Correct Answer: 132, one hundred and thirty two, 132°

## Exit quiz

### 6 Questions

Q1.
Angles on the same side of the transversal line and in between the two other lines are called angles.
alternate
corresponding
vertically opposite
Q2.
Which algebraic statement correctly expresses $$y$$ in terms of $$x$$?
$$y=x$$
$$y= {x\over2}$$
Correct answer: $$y=180-x$$
$$y=360-x$$
Q3.
Which algebraic statement correctly expresses $$y$$ in terms of $$x$$?
$$y=2x$$
$$y=270-x$$
Correct answer: $$y=270-2x$$
$$y=360-x$$
$$y=360-2x$$
Q4.
In which diagram is $$y=180-x$$?