The diagram on the right shows a circle - Junior Cycle Mathematics - Question 9 - 2019

To find angle X in the triangle ABC, we can use the properties of angles in a triangle and the fact that angle ACB is inscribed.

1. Since BC is the diameter of the circle, angle ABC is a right angle (90°) due to the inscribed angle theorem.

2. The sum of angles in triangle ABC is given by: $ext{Angle A} + ext{Angle B} + ext{Angle C} = 180°$

3. We have: $90° + 35° + X = 180°$

4. Rearranging gives: $X = 180° - (90° + 35°)$ $X = 180° - 125°$ $X = 55°$

Thus, the size of the angle X is 55°.