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In the given figure, `angleXYZ=56^(@)` and XY is produced to a point P. If ray YQ bisects `angleZYP`, find `angleXYQ` and reflex `angleQYP`. |
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Answer» Since XY is produced to point P, it follows that XP is a straight line and ray YZ stands on it. `:. angleXYZ+angleZYP=180^(@)` `implies 56^(@)+angleZYP=180^(@)` `implies angleZYP=(180^(@)-56^(@))=124^(@)` `implies angleZTQ=1/2 angleZTP=(1/2xx124^(@))=62^(@)`. `:. angleXYQ=angleXYZ+angleZYQ=(56^(@)+62^(@))=118^(@)`. Also, `angleQYP=1/2 angleZYP=(1/2xx124^(@))=62^(@)` `:.` reflex `angleQYP=360^(@)-angleQYP=(360-62)^(@)=298^(@)`. |
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