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The diagram shows triangle ABC - Edexcel - GCSE Maths - Question 7 - 2019 - Paper 1

Question 7

The diagram shows triangle ABC. ADB is a straight line. the size of angle DCB : the size of angle ACD = 2 : 1 Work out the size of angle BDC.

Worked Solution & Example Answer:The diagram shows triangle ABC - Edexcel - GCSE Maths - Question 7 - 2019 - Paper 1

Step 1

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Answer

To find angle ACD, first note that the angles around point D must sum to 180°. Therefore, we can write:

$ext{Angle ACD} = 180° - 75° - 51° = 54°$

Thus, angle ACD is 54°.

Step 2

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Answer

The ratio of angle DCB to angle ACD is given as 2:1. Let the size of angle DCB be 2x and the size of angle ACD be x:

$ext{Angle DCB} = 2x$ $ext{Angle ACD} = x$

Given that angle ACD is 54°, we can set up the equation:

$x = 54°$

Thus, substituting this back, we find:

$ext{Angle DCB} = 2(54°) = 108°$ .

Step 3

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Answer

Now to find angle BDC, we again apply the angles around point D:

$ext{Angle BDC} = 180° - ( ext{Angle DCB} + ext{Angle ACD})$

Substituting the values we have:

$ext{Angle BDC} = 180° - (108° + 54°) = 180° - 162° = 18°.$

Therefore, the size of angle BDC is 18°.

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