Q132 of 158 Page 159

In Δ DEF, ∠D = 60°, ∠E = 70° and the bisectors of ∠E and ∠F meet at O. Find

(i) ∠F


(ii) ∠EOF.

Given: ∠D = 60°, ∠E = 70°


Formula Used/Theory:-


→ Angle sum property


Sum of all angles of triangle is 180°


In Δ DEF


∠D + ∠E + ∠F = 180°


60° + 70° + ∠F = 180°


∠F = 180° - 130° = 50°


Bisector of ∠E will be 35°


Bisector of ∠F will be 25°


Joining the bisector of ∠E and ∠F at O will make a Δ EOF


Where ∠OEF = 35°


And ∠OFE = 25°


By angle sum property


∠OEF + ∠OFE + ∠EOF = 180°


∠EOF + 35° + 25° = 180°


∠EOF = 180° - 60° = 120°


Result:- ∠EOF = 120°


∠F = 50°


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