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 $123^\circ$.
Related Questions
Know More about
Staff Selection Commission Sub Inspector ...
Result | Eligibility | Application | Selection Process | Cutoff | Admit Card | Preparation Tips
Get Updates Brochure
Your Staff Selection Commission Sub Inspector Exam brochure has been successfully mailed to your registered email id “”.
