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(Exterior Angle Theorem): If a side of a...

(Exterior Angle Theorem): If a side of a triangle is produced, the exterior angle so formed is equal to the sum of the two interior opposite angles. GIVEN : A triangle `A B C,D` is a point of `B C` produced, forming exterior angle `/_4.` TO PROVE : `/_4=/_1+/_2` i.e. , `/_A C D=/_C A B+/_C B Adot`

Text Solution

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Observe that `/_1` and `/_2` together form a straight line.
`/_1+/_2=180`
`/_2=180-/_1`
Sum of all angles of trianle is 180.
`/_A+/_B+/_2=180`
`/_2=180-/_A-/_B`
Thus, ...
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  • The exterior angle of a triangle is 105^(@) and one of the interior opposite angles is 60^(@) . Find the other two angles.

    A
    `45^(@),45^(@)`.
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    A
    `40^(@),60^(@),80^(@)`.
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    `40^(@),40^(@),60^(@)`.
    C
    `40^(@),70^(@),70^(@)`.
    D
    `30^(@),70^(@),80^(@)`.

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