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The diagram shows a straight line crossing two parallel lines - OCR - GCSE Maths - Question 23 - 2021 - Paper 1

Question 23

The diagram shows a straight line crossing two parallel lines. Find the value of y. You must show your working.

Worked Solution & Example Answer:The diagram shows a straight line crossing two parallel lines - OCR - GCSE Maths - Question 23 - 2021 - Paper 1

Step 1

(2x + 30)° + (x + 85)° + y° = 180°

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Answer

To find the value of y, we can use the fact that the angles formed by the transversal crossing parallel lines are supplementary. Hence, we can set up the equation:

$(2x + 30) + (x + 85) + y = 180$

This simplifies to:

$2x + x + 30 + 85 + y = 180$

Combining like terms gives:

$3x + y + 115 = 180$

Now, solving for y:

$y = 180 - 3x - 115$

So:

$y = 65 - 3x$

Step 2

Substituting for x

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Answer

Assuming from the problem (not provided in the question), let’s say we know a value for x, such as if x = 10, then:

$y = 65 - 3(10) = 65 - 30 = 35$

Therefore, for x = 10, y would be 35. Depending on the provided value of x, y can be calculated similarly.

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