Answer: x= 112°, y = 34°
Step-by-step explanation:
"Angles formed by drawing lines from the ends of the diameter of a circle to its circumference form a right angle."
- That means the angle adjacent to 56° = 90° - 56° = 34°
"The angle formed at the centre of the circle by lines originating from two points on the circle's circumference is double the angle formed on the circumference of the circle by lines originating from the same points."
- The angle adjacent to the left of ∠X = 2(34°) = 68°
x = 180° - 68° = 112°
- The angle adjacent to the right of ∠X = the angle adjacent to the right of ∠X = 68°
y = 68 ÷ 2 = 34°
Circle theorems source: https://revisionmaths.com/gcse-maths-revision/shape-and-space/circle-theorems#:~:text=Angles%20formed%20by%20drawing%20lines%20from%20the%20ends,the%20point%20on%20the%20circumference%20our%20triangle%20touches.
