In ∆DEF, ∠D = 60°, ∠E = 70° and the bisectors of ∠E and ∠F meet at O. Find ∠EOF.
Solution:
Given, DEF is a triangle
∠D = 60° and ∠E = 70°
The bisectors of ∠E and ∠F meet at O.
We have to find the measure of ∠EOF.
Angle sum property of a triangle states that the sum of all three interior angles of a triangle is always equal to 180 degrees.
∠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°
✦ Try This: In ∆PQR, ∠P = 50°, ∠Q = 60° and the bisectors of ∠Q and ∠R meet at O. Find ∠QOR.
☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 6
NCERT Exemplar Class 7 Maths Chapter 6 Problem 132 (ii)
In ∆DEF, ∠D = 60°, ∠E = 70° and the bisectors of ∠E and ∠F meet at O. Find ∠EOF.
Summary:
In ∆DEF, ∠D = 60°, ∠E = 70° and the bisectors of ∠E and ∠F meet at O. The values of ∠EOF is 120°.
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