Mathematics

Two lines $AB$ and $CD$ intersect each other at a point $O$ such that $\angle AOC:\angle AOD=5:7$. Find all the angles.

SOLUTION
Consider $\angle AOC$ as $5x$ and $\angle AOD$ as $7x$
from the figure we know that $\angle AOC$ and $\angle AOD$ for linear pair of angle

so it can be written as

$\angle AOC+\angle AOD={ 180 }^{ o }$

by substituting the values

$5x+7x={ 180 }^{ o }$

$x=180/12$

$x={15}^{o}$

by susbtituting the value of $x$

$\angle AOC=5x$

so we get

$\angle AOC=5(15)={75}^{o}$

$\angle AOD=7x$

so we get

$\angle AOD=7(15)={105}^{o}$

from the figure we know that $\angle AOC$ and $\angle BOD$ are vertical angles

so we get

$\angle AOC=\angle BOD={75}^{o}$

from the figures we know that $\angle AOD$ and $\angle BOC$ are vertical angles

so we get

$\angle AOD=\angle BOC={105}^{o}$

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Subjective Medium Published on 09th 09, 2020
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Subjects 10
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