The points A, B, C and D lie on a circle - Edexcel - GCSE Maths - Question 19 - 2019 - Paper 2
Question 19
The points A, B, C and D lie on a circle.
CDE is a straight line.
B A = B D
C B = C D
Angle A B D = 40°
Work out the size of angle A D E.
You must give a reason f... show full transcript
Worked Solution & Example Answer:The points A, B, C and D lie on a circle - Edexcel - GCSE Maths - Question 19 - 2019 - Paper 2
Step 1
Find angle B D E
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Answer
To find angle B D E, we can use the property of angles at the circumference. Since B A = B D (given), triangle A B D is isosceles. Therefore:
∠BDE=180°−∠ABD−∠ADE
Substituting the known values:
∠BDE=180°−40°−∠ADE
Step 2
Find angle B D C
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Answer
Since C B = C D (given), triangle B C D is isosceles as well. Thus, we can calculate angle B D C:
∠BDC=180°−∠DBC−∠BCD=180°−40°=140°
Step 3
Conclusion for angle A D E
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Answer
Finally, sum angles B D E and B D C to prove the supplementary angles:
∠ADE+∠BDC=180°
Substituting values:
∠ADE+140°=180°
Thus, we find:
∠ADE=180°−140°=40°
Consequently, the angle A D E is 75°.
