Question

State true or false:

O is a point inside the triangle ABC. Such that : $\angle BOC=\angle BAC+\angle ABO+\angle ACO$

• A. True
• B. False

Answer 1

The correct option is A True

In $△ABC$,
$\angle ABC+\angle BAC+\angle ACB=180$
In $△OBC$,
$\angle BOC+\angle OCB+\angle OBC=180$
Equating the two equations,
$\angle ABC+\angle BAC+\angle ACB=\angle BOC+\angle OCB+\angle OBC$
$\angle BOC=\angle BAC+(\angle ABC-\angle OBC)+(\angle ACB-\angle OCB)$
$\angle BOC=\angle BAC+\angle ABO+\angle ACO$