This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

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You're on a roll — Step 1: Determine the size of in terms of . Given that . When two parallel chords are intersected by a transversal chord, the alternate interior angles are equal. Consider EG as a transversal intersecting parallel chords and . Therefore, (alternate interior angles). We are given . Thus, .
The size of in terms of is .
Step 2: Calculate the size of $\angle DHG
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You're on a roll — Step 1: Determine the size of DEG in terms of x. Given that DE FG.
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.