Question

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

Answer 1

$\textbf{\huge{ANSWER:}}$

$\sf{Given:}$

Angle D = 60°

Angle E = 70°

According to the angle sum property:

=》 Angle ( D + E + F ) = 180°

=》 Angle F + 60° + 70° = 180°

=》 Angle F = 180° - 130°

=》 $\textbf{Angle F = 50°}$

Angle OFE = OFD = $\frac{50°}{2}$ = 25°( Bisectors, Given )

Angle OEF = OED = $\frac{70°}{2}$ = 35°( Bisectors, Given )

=》 In Triangle OEF, the angle sum property :-

=》 Angle ( EOF + OEF + OFE ) = 180°

=》 Angle EOF + 25° + 35° = 180°

=》 Angle EOF = 180° - 60°

=》 $\textbf{Angle EOF = 120°}$

Answer 2

Answer:

by angle sum property

∠D + ∠E + ∠F = 180°

60° + 70° + ∠F = 180°

130° + ∠F = 180°

∠F = 180° - 130°

Therefore, ∠F = 50°

Since FO is the bisector or ∠F,

∠EFO = ∠F/2 = 50°/2

So, ∠EFO = 25°

Since EO is the bisector of ∠E,

∠OEF = ∠E/2 = 70°/2

So, ∠OEF = 35°

Considering triangle OEF,

By angle sum property,

∠EOF + ∠EFO + ∠OEF = 180°

∠EOF + 25° + 35° = 180°

∠EOF + 60° = 180°

∠EOF = 180° - 60°

Therefore, ∠EOF = 120°