In , =30^ , =40^ and =110^ . The angles of the triangle formed by… - Vidyadip

MCQ

In $\triangle\text{ABC},\angle\text{A}=30^\circ,\angle\text{B}=40^\circ$ and $\angle\text{C}=110^\circ.$ The angles of the triangle formed by joining the mid-points of the sides of this triangle are:

A
$70^\circ , 70^\circ , 40^\circ $
B
$60^\circ , 40^\circ , 80^\circ $
✓
$30^\circ , 40^\circ , 110^\circ$
D
$60^\circ , 70^\circ , 50^\circ$

✓

Answer

Correct option: C.

$30^\circ , 40^\circ , 110^\circ$

If in any triangle, all the mid-points (of each sides) are joined to form a triangle, then that triangle is similian to a parent triangle.
i.e.$\triangle\text{QPR}\sim\triangle\text{ABC}$
So angles of $\triangle\text{PQR}$ will be same as angles of $\triangle\text{ABC}.$
Thus, angles are $30^\circ , 40^\circ , 110^\circ $

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