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The diagram shows two intersecting straight lines - OCR - GCSE Maths - Question 20 - 2019 - Paper 2

Question 20

The diagram shows two intersecting straight lines. Find the value of y. $(x + 20)^{\circ}$ and $(3x - 50)^{\circ}$ are the angles opposite each other at the inters... show full transcript

Worked Solution & Example Answer:The diagram shows two intersecting straight lines - OCR - GCSE Maths - Question 20 - 2019 - Paper 2

Step 1

Find the relationship between angles

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Answer

Since the angles $(x + 20)^{\circ}$ and $(3x - 50)^{\circ}$ are vertically opposite, we can set them equal to each other:

$x + 20 = 3x - 50$

Step 2

Solve for x

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Answer

Rearranging the equation gives:

$20 + 50 = 3x - x$

$70 = 2x$

Dividing both sides by 2 results in: $x = 35$

Step 3

Substitute x back to find y

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Answer

Now substituting $x = 35$ into the expression for $y$ :

$y = x + 20 = 35 + 20 = 55$

Thus, the value of $y$ is 55.

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