Angles in Polygons & Parallel Lines (OCR GCSE Maths: Higher): Exam Questions

Work out the size of the exterior angle of a regular 12-sided polygon.

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Use your answer to part (a) to write down the size of the interior angle of a regular 12-sided polygon.

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The diagram shows triangle ABC.
CD is parallel to AB.
A, C and E lie in a straight line.
Angles of size and are shown.

Insert  ° or to make this statement true. Give a reason for your answer.

Angle DCE = ......... because ....................................................................................................

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Use the diagram and the answer to part (a) to show that the angles of a triangle add up to 180°.

Give a reason for each statement you make.

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Here is a 10-sided polygon.

Work out the value of 

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Each interior angle of a regular polygon is 162°

Work out the number of sides the polygon has.

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The diagram shows a triangle.

Work out the value of .

= ..................

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The diagram shows a parallelogram  and an isosceles triangle  in which 

and  are straight lines.
Angle 

Work out the size of angle 
Give a reason for each stage of your working.

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What is the size of an exterior angle of a regular decagon?

Circle your answer.

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The exterior angle of a regular polygon is 45°

Circle the name of the regular polygon.

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Part of a regular polygon with 15 sides is shown.

Work out the size of an interior angle.

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The sum of the angles in any quadrilateral is 360°

For example, in a rectangle 4 × 90° = 360°

Zak writes,

   5 × 90° = 450° so the sum of the angles in any pentagon must be 450°

Is he correct?

Tick a box.

       Yes          No

Show working to support your answer.

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