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

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 ∠F.

Angle sum property of a triangle states that the sum of all three interior angles of a triangle is always equal to 180 degrees.

By angle sum property,

∠D + ∠E + ∠F = 180°

60° + 70° + ∠F = 180°

130° + ∠F = 180°

∠F = 180° - 130°

Therefore, ∠F = 50°

Therefore, ∠EOF = 120°

✦ Try This: In ∆PQR, ∠P = 50°, ∠Q = 60° and the bisectors of ∠Q and ∠R meet at O. Find ∠R.

☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 6

NCERT Exemplar Class 7 Maths Chapter 6 Problem 132 (i)

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

Summary:

In ∆DEF, ∠D = 60°, ∠E = 70° and the bisectors of ∠E and ∠F meet at O. The values of ∠F is 50°.

☛ Related Questions:

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