Read the following two statements which are taken as axiom:
(i) If two lines intersect each other , then the vertically opposite angles are not equal.
(ii) If a ray stands on a line , then the sum of two adjacent angles, so formed is equal to `180^(@)`.
Is this system of axioms consistent ? Justify your answer.

Explanation

We know that , if two lines intersect each other, then the vertically opposite angles are equal. It is a theorem , So given Statement I is false and not an axiom.
We know that , if a ray stands on a line, then the sum of two adjacent angles so formed is equal to `180^(@)` . It is an axiom . So given Statement II is true and an axiom.
Thus, in given statements first is fales and second is an axiom . Hence , given system of axioms is consistent.