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20 A, B, C and D are points on the circumference of a circle, centre O - Edexcel - GCSE Maths - Question 20 - 2022 - Paper 2

Question 20

20 A, B, C and D are points on the circumference of a circle, centre O. ADE and BCE are straight lines. Work out the size of angle CDE. Give a reason for each stage... show full transcript

Worked Solution & Example Answer:20 A, B, C and D are points on the circumference of a circle, centre O - Edexcel - GCSE Maths - Question 20 - 2022 - Paper 2

Step 1

Find angle AOD

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Answer

We know that angle AOD is created by lines AO and OD. Since angle ADB is an exterior angle to triangle ACB, it can be calculated as follows:

$AOD = 360^ ext{o} - 132^ ext{o} - 16^ ext{o} = 212^ ext{o}$

Step 2

Find angle BOD

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Answer

Using the property that angles at the centre are double the angles at the circumference, we can determine angle BOD:

$BOD = rac{1}{2} imes AOD = rac{1}{2} imes 212^ ext{o} = 106^ ext{o}$

Step 3

Calculate angle CDE

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Answer

Since angles CDE and BOD are vertically opposite, we can conclude that:

$CDE = BOD = 106^ ext{o}$

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