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: $143^{\circ}$

Question

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: $143^{\circ}$

Team Careers360 · Accepted Answer

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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Question : E, F, G, and H are four points lying on the circumference of a circle to make a cyclic quadrilateral. If ∠FGH=57∘, then what will be the measure of the ∠HEF?Option 1: 33∘Option 2: 123∘Option 3: 93∘Option 4: 143∘

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Question : E, F, G, and H are four points lying on the circumference of a circle to make a cyclic quadrilateral. If $∠ F G H = 57^{\circ}$ , then what will be the measure of the $∠ H E F$ ?
Option 1: $33^{\circ}$
Option 2: $123^{\circ}$
Option 3: $93^{\circ}$
Option 4: $143^{\circ}$