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In the given figure, l||m and a transver...

In the given figure, `l||m` and a transversal t cuts them. If `angle1=70^(@)`, find the measure of each of the remaining marked angles.

Text Solution

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Clearly, a ray t stands on line l making adjacent angles `angle1` and `angle2`
`:. angle1+angle2=180^(@) implies 70^(@)+angle2=180^(@)`
`implies angle2=(180^(@)-70^(@))=110^(@)`.
`:. Angle4=angle2=110^(@)` [vertically opposite `angles`]
and `angle3=angle1=70^(@)` [vertically opposite `angles`].
Now, `l||m` and t is the transversal.
`:. angle5=angle3=70^(@)` [alternate interior `angles`]
`angle6=angle4=110^(@)` [alternate interior `angles`]
`angle7=angle3=70^(@)` [corresponding `angles`]
and `angle8=angle4=110^(@)` [correspoding `angles`].
`:. angle2=110^(@), angle3=70^(@), angle4=110^(@), angle5=70^(@), angle6=110^(@)`,
`angle7=70^(@) and angle8=110^(@)`.
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