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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, we first calculate angle ADB. Since ADB is a straight line, it can be calculated as follows:

ext{angle ADB} = 180^ ext{o} - (75^ ext{o} + 51^ ext{o}) = 180^ ext{o} - 126^ ext{o} = 54^ ext{o}

Using the given ratio of angles, let the size of angle ACD be represented as x. Therefore, DCB is 2x. Since ACD and DCB add up to angle ADB:

ext{angle ACD} + ext{angle DCB} = ext{angle ADB},\ herefore x + 2x = 54^ ext{o}

This simplifies to:

3x = 54^ ext{o}

Thus,

x = rac{54^ ext{o}}{3} = 18^ ext{o}

Step 2

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Answer

Using the ratio, the size of angle DCB is:

ext{angle DCB} = 2x = 2 imes 18^ ext{o} = 36^ ext{o}.

Step 3

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Answer

Finally, to find the size of angle BDC, we can use the fact that the sum of angles in a triangle equals 180 degrees. In triangle BDC:

ext{angle BDC} + ext{angle DBC} + ext{angle DCB} = 180^ ext{o}

We already have angle DBC as 51 degrees and angle DCB as 36 degrees:

ext{angle BDC} + 51^ ext{o} + 36^ ext{o} = 180^ ext{o}

Thus,

ext{angle BDC} = 180^ ext{o} - (51^ ext{o} + 36^ ext{o}) = 180^ ext{o} - 87^ ext{o} = 93^ ext{o}.

Therefore, the size of angle BDC is 93 degrees.