Question

In ΔDEF, ∠D = 60°, ∠E = 70° and the bisectors of ∠E and ∠F meet at O. Find (i) ∠F (i) ∠EOF.

Answer 1

(i) As we know,

∠D + ∠E + ∠F = 180° ......[Angle sum property of a triangle]

⇒ 60° + 70° + ∠F = 180°  ......[∵ ∠D = 60° and ∠E = 70°]

⇒ ∠F = 180° – 130°

⇒ ∠F = 50°

(ii) Now, as FO is the bisector of ∠F

So, ∠EFO = `(∠F)/2 = 50^circ/2` = 25°

And ∠OEF = `(∠E)/2 = 70^circ/2` = 35°  ......[∵ ∠D = 60° and ∠E = 70°]

In ΔEOF, ∠EOF + ∠OEF + ∠OFE = 180°  ......[Angle sum property of a triangle]

⇒ ∠EOF + 35° + 25° = 180°

⇒ ∠EOF = 180° – 60°

⇒ ∠EOF = 120°