Problem solving with polygons | Maths | Quizalize & Oak National Academy

Starter quiz

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

∠BCD and ∠CEF

⇔

corresponding angles ✓

∠ACE and ∠HEC

⇔

co-interior angles ✓

∠ACE and ∠CEF

⇔

alternate angles ✓

∠HEC and ∠GEF

⇔

vertically opposite angles ✓
A dodecagon has 12 sides. Find the sum of the interior angles in a dodecagon.

180°

360°

1800° ✓

2160°

2520°
Exterior angles for any polygon sum to ______°.

'360' ✓
Each exterior angle for a regular hexagon is ______°.

'60' ✓
Each interior angle in a regular octagon is ______°.

'135' ✓
The pentagon and hexagon in the diagram are both regular. The angle marked in the diagram is ______°.

'132' ✓

Angles on the same side of the transversal line and in between the two other lines are called ______ angles.

alternate

co-interior ✓

corresponding

vertically opposite
Which algebraic statement correctly expresses $y$ in terms of $x$ ?

$y=x$

$y= {x\over2}$

$y=180-x$ ✓

$y=360-x$
Which algebraic statement correctly expresses $y$ in terms of $x$ ?

$y=2x$

$y=270-x$

$y=270-2x$ ✓

$y=360-x$

$y=360-2x$
In which diagram is $y=180-x$ ?
The size of the angle marked in the diagram is ______°.

'30' ✓
The size of the angle marked in the diagram is ______°.

'60' ✓

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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.

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.