20 A, B, C and D are points on the circumference of a circle, centre O - Edexcel - GCSE Maths - Question 21 - 2022 - Paper 2
Question 21
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 21 - 2022 - Paper 2
Step 1
Calculate angle DAB
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Answer
Given that angle ADB is given as 132°, we can determine angle DAB by the fact that angles at the circumference subtended by the same arc are equal. Therefore,
DAB=21×132°=66°.
Step 2
Calculate angle DCE
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Answer
In triangle DAB, the angles sum to 180 degrees. Therefore, we can find angle DCE:
DCE=180°−DAB−ADB=180°−66°−132°=−18°.
But we are not concerned about angle DCE here directly.
Step 3
Find angle CDE
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Answer
Using the cyclic properties of a circle, the opposite angles of cyclic quadrilaterals sum to 180°. Therefore:
