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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 CdotD` 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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`In /_ABC`
`/_1+/_2+/_3=180^@-(1)`
`/_3+/_4=180^@-(2)`
from equation 1 and 2
`/_1+/_2+/_3=/_3+/_4`
`/_1+/_2=/_4`
`/_CAB+/_CBA=/_ACD`.
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Knowledge Check

  • one side of a triangle is produced and the exterior angle so formed is 140^@ . If the interior opposite angles are in the ratio. 2:5, find the measure of each angle of the triangle.

    A
    `40^@, 75^@, 60^@`
    B
    `40^@, 70^@, 70^@`
    C
    `40^@, 100^@, 40^@`
    D
    `40^@, 75^@, 65^@`

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    one side of a triangle is produced and the exterior angle so formed is 120^(@) .if the interior opposite angles be in the ratio 3:5 .find the measure of each angles of triangle .

    If the exterior angle of a triangle is 130° and its interior opposite angles are equal, then measure of each interior opposite angle is

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