Question : E, F, G, and H are four points lying on the circumference of a circle to make a cyclic quadrilateral. If $\angle {FGH}=57^{\circ}$, then what will be the measure of the $\angle {HEF}$?
Option 1: $33^{\circ}$
Option 2: $123^{\circ}$
Option 3: $93^{\circ}$
Option 4: $143^{\circ}$
Correct Answer: $123^{\circ}$
Solution : E, F, G, and H form a cyclic quadrilateral. $\angle {FGH}=57^{\circ}$ In a cyclic quadrilateral, the sum of opposite angles is 180$^\circ$. So, $\angle {FGH} + \angle {HEF} = 180^\circ$ ⇒ $57^{\circ} + \angle {HEF} = 180^\circ$ ⇒ $\angle {HEF} = 180^\circ- 57^{\circ} = 123^\circ$ Hence, the correct answer is $123^\circ$.
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