Mathematics

# In the figure, three coplanar lines $AB,CD$ and $EF$ intersect at a point $O$, forming angles as shown. Find the values of $x,y,z$ and $t$

##### SOLUTION
From the figure we know that $\angle COE$ and $\angle DOF$ are vertically opposite angles

$\angle COE=\angle DOF=\angle z={50}^{o}$

From the figure we know that $\angle BOD$ and $\angle COA$ are vertically opposite angles

$\angle BOD=\angle COA=\angle t={90}^{o}$

We also know that $\angle COA$ and $\angle AOD$ form a linear pair

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

It can also be written as

$\angle COA+\angle AOF+\angle FOD={ 180 }^{ o }$

By substituting the values we get

${90}^{o}+{x}^{o}+{50}^{o}={ 180 }^{ o }$

${x}^{o}={40}^{o}$

From the figure we know that $\angle EOB$ and $\angle AOF$ are vertically opposite angles

$\angle EOB=\angle AOF=x=y=40$

Therefore the values of $x,y,z,t$ are $40^{o},40^{o},50^{o},90^{o}$

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Subjective Medium Published on 09th 09, 2020
Questions 120418
Subjects 10
Chapters 88
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