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In the diagram, AB is parallel to DC - OCR - GCSE Maths - Question 7 - 2018 - Paper 1

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Question 7

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In the diagram, AB is parallel to DC. Work out angle BDC. Give a reason for each angle you work out. The angles are given as 56° and 80° in the diagram.

Worked Solution & Example Answer:In the diagram, AB is parallel to DC - OCR - GCSE Maths - Question 7 - 2018 - Paper 1

Step 1

Work out angle ABC

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Answer

Angle ABC can be calculated using the fact that AB is parallel to DC. Therefore, the alternate angle to angle DAB (which is 80°) is equal to angle ABC. Thus, we have:

ABC=80°ABC = 80°

Reason: Alternate angles are equal when a transversal crosses parallel lines.

Step 2

Work out angle ACD

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Answer

Angle ACD can be calculated as the sum of angles in a triangle. In triangle ABC, we know:

  • Angle ABC = 80°
  • Angle ACB = 56°

Using the triangle sum property:

A+B+C=180°A + B + C = 180°

Therefore:

80°+56°+ACD=180°80° + 56° + ACD = 180°

Rearranging gives:

ACD=180°−80°−56° =44°ACD = 180° - 80° - 56° \ = 44°

Reason: Angles in a triangle sum to 180°.

Step 3

Work out angle BDC

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Answer

Finally, angle BDC is calculated as follows:

BDC=ACD =44°BDC = ACD \ = 44°

Reason: Angles between parallel lines (exterior angles) are equal.

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