Question

In triangle abc find the measure of angles form by joining the

Answer 1

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Given : ABC is a triangle with ∠A = 40°, ∠B = 80°, ∠C = 60°.

Let D, E, F be the mid points of side BC, AC, AB respectively.

Now according to mid point theorem, The line segments joining the mid points of the sides of a triangle is parallel to the third side of triangle.

⇒ FE // BC

⇒ FE // BD and FE // DC  ..... (1)

ED // AB

⇒ ED // AF and ED // FB  ..... (2)

FD // AC

⇒ FD // AE and FD // EC  ..... (3)

from (1), (2) and (3) we can conclude that

AFDE, BFED, DFEC are parallelogram.

Also opposite angles of a parallelogram are equal

⇒ ∠FAE = ∠FDE = 40°

⇒ ∠FBD = ∠FED = 80°

⇒ ∠DCE = ∠DFE = 60°

∴ In ΔDEF

∠D = 40°, ∠E = 80° and ∠F = 60°

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