The diagram shows a circle, centre O - OCR - GCSE Maths - Question 19 - 2018 - Paper 5

To find the value of $x$ in triangle ODC, we can use the relationship between angles on a straight line and the properties of angles in a circle.

1. Since EDF is a tangent to the circle, we know that angle ODF is $90^ ext{o}$.
2. In triangle ODC, we know the angles:
   • Angle ODC = $57^ ext{o}$
   • Angle ODF = $90^ ext{o}$
3. To calculate angle AOD: $AOD = 180^ ext{o} - (ODC + ODF) = 180^ ext{o} - (57^ ext{o} + 90^ ext{o}) = 33^ ext{o}$
4. Using angle ABC = $82^ ext{o}$: $x + 33^ ext{o} = 82^ ext{o}$
5. Therefore, solving for $x$: $x = 82^ ext{o} - 33^ ext{o} = 49^ ext{o}$

Thus, the value of $x$ is 49°.