Math  /  Geometry

QuestionIt is given that XYZ=64\angle \mathrm{XYZ}=64^{\circ} and XY is produced to point P . Draw a figure from the given information. If ray YQ bisects ZYP\angle \mathrm{ZYP}, find XYQ\angle \mathrm{XYQ} and reflex QYP\angle \mathrm{QYP}.

Studdy Solution
Calculate the reflex QYP\angle \mathrm{QYP}.
The reflex angle is the larger angle formed around point Y, excluding QYP\angle \mathrm{QYP}: Reflex QYP=360QYP\text{Reflex } \angle \mathrm{QYP} = 360^{\circ} - \angle \mathrm{QYP}
Since QYP\angle \mathrm{QYP} is half of ZYP\angle \mathrm{ZYP}: QYP=58Reflex QYP=36058=302\angle \mathrm{QYP} = 58^{\circ} \\ \text{Reflex } \angle \mathrm{QYP} = 360^{\circ} - 58^{\circ} = 302^{\circ}
The final results are: XYQ=58Reflex QYP=302\angle \mathrm{XYQ} = 58^{\circ} \\ \text{Reflex } \angle \mathrm{QYP} = 302^{\circ}

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