(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
Verified by Experts
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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