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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 : angle2=5 :4`, find the measure of each of the marked angles.

Text Solution

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Let `angle1=(5x)^(@) and angle2=(4x)^(@)`.
Clearly, the ray t stands on line `l`.
`:. Angle1+angle2=180^(@) implies 5x+4x=180`
`implies 9x=180 implies x=20`
`:. Angle1=(5xx20)^(@)=100^(@) and angle2=(4xx20)^(@)=80^(@)`.
Now, `angle3=angle2=100^(@)` [vertically opposite `angles`]
`angle4=amgle2=80^(@)` [vertically opposite `angles`].
Now, `l||m` and t is the transversal.
`:. angle5=angle3=100^(@)` [alternate interior `angles`]
`angle6=angle4=80^(@)` [alternate interior `angles`]
`angle7=angle3=100^(@)` [corresponding `anfles`]
`angle8=angle4=80^(@)` [corresponding `angles`]
`:. angle1=100^(@), angle2=80^(@), angle3=100^(@), angle4=80^(@)`.
`angle5=100^(@), angle6=80^(@), angle7=100^(@), angle8=80^(@)`.
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