How many dimensions does a line have?

Read the following two statements which are taken as axioms:
$(i)$ 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 $180^{\circ}$.
Is this system of axioms consistent? Justify your answer.

Solve the following question using an appropriate Euclid's axiom:
In the figure,we have $AB = BC$ and $BX = BY$. Show that $AX = CY$.

Given two distinct points,there is a ......... line that passes through them.

In the figure,we have: $AC = XD$,$C$ is the mid-point of $AB$ and $D$ is the mid-point of $XY$. Using Euclid's axiom,show that $AB = XY$.

State whether the following statement is True or False. Justify your answer.
Euclidean geometry is valid only for curved surfaces.