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$\angle{QYP}={360}^{\circ}-\angle{QYP}={360}^{\circ}-{58}^{\circ}={302}^{\circ}$ You're just one step away

Subjective Medium Published on 09th 09, 2020
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