In a triangle ABC, angle A=40^{o,}, angle B=80^{o}, angle C=60^{o}. Find the measures of the angles of the angles of the triangles formed by joining the midpoints of this triangle.

**Please answer fast my worksheet is due on monday!!**

Dear Student!

Here is the answer to your query.

**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°

Cheers!

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