Question

In a ΔABC, ∠A = 50°, ∠B = 60° and ∠C = 70°. Find the measures of the angles of the triangle formed by joining the mid-points of the sides of this triangle.

Answer 1

In ΔABC, 

D, E and F are mid points of AB,BC and AC respectively. 

In a Quadrilateral DECF: 

By Mid-point theorem, 

DE ∥ AC ⇒ DE = AC/2 

And CF = AC/2 

⇒ DE = CF 

Therefore, DECF is a parallelogram. 

∠C = ∠D = 70° [Opposite sides of a parallelogram] 

Similarly, 

ADEF is a parallelogram, ∠A = ∠E = 50° 

BEFD is a parallelogram, ∠B = ∠F = 60° 

Hence, Angles of ΔDEF are: ∠D = 70°, ∠E = 50°, ∠F = 60°.