Correct option is D. $$\angle a=\angle d$$
The two lines $$l$$ and $$m$$ shown in the figure forms $$4$$ angles, $$a,\ b,\ c\ and\ d$$.
$$\angle a$$ and $$\angle b$$ are vertically opposite angles.
Hence, $$\angle a=\angle b$$.
Similarly, $$\angle c$$ and $$\angle d$$ are also vertically opposite angles.
Hence, $$\angle d=\angle c$$.
Also, $$\angle a$$ and $$\angle d$$ form a linear pair.
Hence, $$\angle a+\angle d=180^o$$
Since $$\angle a+\angle d=180^o$$, $$\angle a$$ cannot be equal to $$\angle d$$, unless they are both right angles, which is not the case here.
Hence, option D is false here.