Here are the solutions for , Question 1:
The points A, B, C, D, E, F, G, and H all lie on the circumference of the circle. We will use properties of cyclic quadrilaterals and angles subtended by the same arc.
1. Determine w
- Consider the cyclic quadrilateral ABEH.
- The sum of opposite angles in a cyclic quadrilateral is 180∘.
- Therefore, ∠ABE+∠AHE=180∘.
- We are given ∠ABE=120∘.
- So, 120∘+w=180∘.