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^circ`

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