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Question

In the given figure, $$l\parallel m$$ and a transversal $$t$$ cuts them. If $$\angle 1={120}^{o}$$, find the measure of each of the remaining marked angles.

Solution
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It is given that $$\angle 1={120}^{o}$$
from the figure we know that $$\angle 1$$ and $$\angle 2$$ form a linear pair of angles

so it can be written as

$$\angle 1+\angle 2={ 180 }^{ o }$$

by substituting the values

$${120}^{o}+\angle 2={ 180 }^{ o }$$

$$\angle 2={60}^{o}$$

from the figure we know that $$\angle 1$$ and $$\angle 3$$ are vertically opposite angles

we get

$$\angle 1=\angle 3={120}^{o}$$

from the figure we know that $$\angle 2$$ and $$\angle 4$$ are vertically opposite angles

we get

$$\angle 2=\angle 4={60}^{o}$$

it is given that $$l\parallel m$$ and $$t$$ is a transversal

so the corresponding angles according to the figures is written as

$$\angle 1=\angle 5={120}^{o}$$

$$\angle 2=\angle 6={60}^{o}$$

$$\angle 3=\angle 7={120}^{o}$$

$$\angle 4=\angle 8={60}^{o}$$

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