Mathematics

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


SOLUTION
$$XYP$$ is a straight line,

$$\angle{XYZ}+\angle{ZYP}={180}^{\circ}$$(linear pair)

$$\angle{ZYP}={180}^{\circ}-\angle{XYZ}={180}^{\circ}-{64}^{\circ}={116}^{\circ}$$

Since $$YQ$$ bisects $$\angle{ZYP}$$

$$\angle{ZYQ}=\angle{QYP}=\dfrac{1}{2}\angle{ZYP}=\dfrac{1}{2}\times {116}^{\circ}={58}^{\circ}$$

$$\angle{XYQ}=\angle{XYZ}+\angle{ZYQ}={64}^{\circ}+{58}^{\circ}={122}^{\circ}$$

We have to find reflex$$\angle{QYP}$$

Reflex$$\angle{QYP}={360}^{\circ}-\angle{QYP}={360}^{\circ}-{58}^{\circ}={302}^{\circ}$$
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Subjective Medium Published on 09th 09, 2020
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