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Question -

In a triangle ∠ABC, ∠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 -

It is given that D, E and F be the mid-points of BC , CA and AB respectively.

Then,

, and .

Now,  and transversal CB and CA intersect themat D and E respectively.

Therefore,

 [(Given)]

and 

 [(Given)]

Similarly, 

Therefore,

[(Given)]

and 

 [(Given)]

Similarly, 

Therefore,

 [(Given)] and 

[(Given)]

Now BC is a straightline.

Similarly, 

and 

Hencethe measure of angles are , and.

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