Question

In ΔABC, 

∠A =30°, 

∠B=40° and 

∠C=110°. 

The angles of the triangle formed by joining the mid-points of the sides of this triangle are 

A. 70°, 70°, 40° 

B. 60°, 40°, 80° 

C. 30°, 40°, 110° 

D. 60°, 70°, 50°

Answer 1

Option : (C)

Given, 

In ∆ABC

∠A = 30°,∠B = 40°,∠C = 110°

In figure, 

BDEF,DCEF,DEAF are parallelograms 

So, 

∠B = ∠E = 40° 

[∵∠B&∠E are opposite angles of parallelogram BDEF]

∠C =∠F = 110° 

[ ∵ ∠C &∠F are opposite angles of parallelogram DCEF]

∠A =∠D =30° 

[ ∵∠A &∠D are opposite angles of parallelogram DEAF]

Hence, 

∠D = 30° 

∠E = 40° 

∠F = 110°