1 Given B2 = x. Prove that E1, D1 and F1 also equal x. 8.2 Calculate angle CBE.

Here's the solution to the question:

8.1) Given $\hat{B}_2 = x$.
The three other angles equal to $x$ are:

• $\hat{E}_1 = x$ (Angle between tangent $CA$ and chord $BE$ is equal to the angle in the alternate segment).
• $\hat{D}_1 = x$ (Angles subtended by the same arc $BD$).
• $\hat{F}_1 = x$ (Alternate angles, $BD \parallel AO$ with transversal $BE$).

8.2)
The angle $C\hat{B}E$ is the angle formed by the tangent $CB$ and the chord $BE$. From the diagram, this angle is