Determine angle $d$ in the Figure below.

A$.b=15($vertical opposite angles are equal$)$

and $a=50($angles$,40$ and a are complementary angles$)$

Therefore $d=65($the exterior angle equals the sum of opposite interior angles of a $\frac{?}{{?}_{\frac{?}{?}}}$

B$.b=15($vertical opposite angles are equal$)$

and $a=50($angles$,40$ and a are complementary angles$)$

$c=115($sum of interior angles of a $\frac{?}{{?}_{\frac{?}{?}}}$ are supplementary$),$ therefore $d=65($adjacent angles, a and $d$ on a straight line are supplementary$)$

C$.b=15($vertical opposite angles are equal$)$

and $a=50($angles$,40$ and a are complementary angles$)$

$c=55($sum of interior angles of a $\frac{?}{{?}_{\frac{?}{?}}}$ are supplementary$),$ therefore $d=125($adjacent angles, a and $d$ on a straight line are supplementary$)$

D$.b=15($vertical opposite angles are equal$),$ therefore $d=15($corresponding angles are equal$)$

E$.$ It is impossible to determine $d$