Calculate the sizes of the following angles: i) DGE

The angle $\angle DGE$ is subtended by arc DE at the circumference. The angle $\angle DBE$ is also subtended by arc DE at the circumference.

Angles subtended by the same arc at the circumference are equal.
Therefore, $\angle DGE = \angle DBE$.

Given $\angle EBD = 27^\circ$, which is the same as $\angle DBE$.

Reason: *Angles