Question

DC < DF
If the above statement is true then mention answer as 1, else mention 0 if false

Answer 1

Given angle BAC is 60 deg and angle ABC is 65 deg.

Hence by angle sum property of a triangle, angle C is 55 deg.

In triangle BEC, angle BEC is 90 deg and angle CBE is 65 deg. Therefore, BCE is 25 deg. This implies angle ECA is 30 deg.

Consider triangle FDC.

Angle FDC is 90 deg as seen in the figure.

Angle FCD is 25 deg [ found above]

Angle DFC is 65 deg [ angle sum property of a triangle]

We know that in a triangle, side opposite a larger angle is larger than the side opposite a smaller angle.

Hence in triangle FDC, angle opposite DC is 65 deg and angle opposite DF is 25 deg.

Therefore, DC > DF.

The above statement that DC < DF is false. Hence 0.