Question

State true or false:

If $DC=BC$ and $\angle y<\angle z$, then $\angle x>2\angle y$.

If true enter 1 else 0

Answer 1

Here angle CDB is exterior angle. and we know,

If one side of a triangle is extended, then the exterior angle is equal to the sum of the opposite interior angles.

So, $\angle z+\angle y=\angle CDB$

$\angle y<\angle z$

$2\ast \angle y<\angle CDB$ ...............eq 1

As DC=BC

so, $\angle CDB=\angle x$ ...............eq 2

from eq 1 and eq 2

$2\ast \angle y<\angle x$

Answer 1