In the diagram, AB is parallel to DC - OCR - GCSE Maths - Question 7 - 2018 - Paper 1
Question 7
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°
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°
Therefore:
80°+56°+ACD=180°
Rearranging gives:
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°
Reason: Angles between parallel lines (exterior angles) are equal.
