14 (a) Three lines meet at a point - OCR - GCSE Maths - Question 14 - 2019 - Paper 1
Question 14
14 (a) Three lines meet at a point.
Work out the size of angle a.
(b) XY and CW are parallel lines.
AB = CB.
Angle CAB = 130°.
(i) Complete this sentence.
Angle ... show full transcript
Worked Solution & Example Answer:14 (a) Three lines meet at a point - OCR - GCSE Maths - Question 14 - 2019 - Paper 1
Step 1
Work out the size of angle a.
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Answer
To find angle a, we know that the sum of angles around a point is 360 degrees. Given the two angles 103° and 100°, we can calculate angle a as follows:
a+103°+100°=360°
Calculating the sum of the known angles:
103°+100°=203°
Now, solve for angle a:
a=360°−203°a=157°
Step 2
Complete this sentence.
Angle CAB = 50° because
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Answer
Angle CAB = 50° because the angles on a straight line sum to 180°. Using the fact that angle AXC is straight:
130°+extAngleCAB=180°
Thus, angle CAB = 50°.
Step 3
Work out angle BCW.
Give a reason for each angle you work out.
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Answer
To find angle BCW, we can use the alternate interior angles theorem. Since XY and CW are parallel lines:
Angle BCW = Angle CAB = 50° because alternate interior angles formed by a transversal cutting through parallel lines are equal.
