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BEG is a triangle: ABC and DEF are parallel lines - Edexcel - GCSE Maths - Question 4 - 2018 - Paper 2
Question 4
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 4 - 2018 - Paper 2
Step 1
Work out the size of angle x using parallel lines
Answer
Since ABC and DEF are parallel lines, we can use corresponding angles. The angle at E (which is 110°) corresponds to angle B in triangle BEG. Therefore:
Angle B = 110°.
Next, we calculate angle G:
In triangle BEG, the sum of the angles is 180°.
Using the known angles, we establish:
110° + 35° + x = 180°.
To find x, we rearrange the equation:
x = 180° - 110° - 35°.
Calculating it gives us: x = 35°.
Thus, angle x measures 35°.
Step 2
Give a reason for your working
Answer
The reason for the calculation of angle x stems from the properties of parallel lines and by applying the angle sum property of a triangle. We identified that angles at a point on parallel lines are equal, allowing us to establish relationships among the angles within triangle BEG.