Photo AI

In the diagram, line AB is parallel to line ED - OCR - GCSE Maths - Question 18 - 2023 - Paper 2

Question 18

In the diagram, line AB is parallel to line ED. The points A, C and D lie on a straight line. The points B, C and E lie on a straight line. Angle BCA = 45°; angle A... show full transcript

Worked Solution & Example Answer:In the diagram, line AB is parallel to line ED - OCR - GCSE Maths - Question 18 - 2023 - Paper 2

Step 1

Angle BCA = 45°

96%

114 rated

Answer

Since line AB is parallel to line ED, we can use the property of alternate angles. Thus, angle ABC is equal to angle CDE because they are corresponding angles. Therefore, we have:

$y = 3k ext{ and } x = 2k$ where $k$ is a common multiplier.

Step 2

Using the interior angles of a triangle

99%

104 rated

Answer

In triangle ABC, the sum of angles should equal 180°:

$45° + x + y = 180°$

Substituting $y = 1.5x$ (from ratio where $y = rac{2}{3} x$ ):

$45 + x + \frac{2}{3}x = 180$

This simplifies to:

$45 + \frac{5}{3}x = 180$

Subtracting 45 gives:

$\frac{5}{3}x = 135$

Multiplying through by $rac{3}{5}$ leads to:

$x = 81°$ .

Step 3

Conclusion

96%

101 rated

Answer

Thus, the value of $x$ is 81°.

Join the GCSE students using SimpleStudy...

97% of Students

Report Improved Results

98% of Students

Recommend to friends

100,000+

Students Supported

1 Million+

Questions answered

;