Solve the equation $a-15=25$ and state which axiom do you use here.

Solve the following question using an appropriate Euclid's axiom:
In the figure,we have $\angle ABC = \angle ACB$ and $\angle 3 = \angle 4$. Show that $\angle 1 = \angle 2$.

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.

If $P$,$Q$,and $R$ are three points on a line,and $Q$ lies between $P$ and $R$ [see figure],then prove that $PQ + QR = PR$.

Solve the following question using appropriate Euclid's axiom:
It is known that $x+y=10$ and that $x=z$. Show that $z+y=10$.

Euclid's fifth postulate is: