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BEG is a triangle: ABC and DEF are parallel lines - Edexcel - GCSE Maths - Question 5 - 2018 - Paper 2

Question 5

BEG is a triangle: ABC and DEF are parallel lines. Work out the size of angle x. Give a reason for each stage of your working.

Worked Solution & Example Answer:BEG is a triangle: ABC and DEF are parallel lines - Edexcel - GCSE Maths - Question 5 - 2018 - Paper 2

Step 1

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Answer

Since ABC and DEF are parallel lines, the angles 110° and angle at E (which is 25°) are co-interior angles. Thus, we have:

$110° + 25° = 135°$

The sum of co-interior angles is equal to 180°. Therefore:

$180° - 135° = 45°$

This means that angle E measures 45°.

Step 2

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Answer

In triangle BEG, we know that the sum of all angles in a triangle is 180°. Hence:

$35° + x + 45° = 180°$

Now, summing 35° and 45° gives:

$80°$

Thus, we can rearrange the equation:

$x = 180° - 80°$

Which simplifies to:

$x = 100°$

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