Answer: The correct option is (A) 95°.
Step-by-step explanation: In the given figure, we have
m∠4 = 120° and m∠2 = 35°.
We are to find the measure of ∠5.
Since ∠3 and ∠4 makes a linear pair, so
[tex]m\angle 3+m\angle 4=180^\circ\\\\\Rightarrow m\angle 3+120^\circ=180^\circ\\\\\Rightarrow m\angle 3=180^\circ-120^\circ\\\\\Rightarrow m\angle 3=60^\circ.[/tex]
The sum of the measures of three angles of a triangle is 180°, so
[tex]m\angle 1+m\angle 2+m\angle 3=180^\circ\\\\\Rightarrow m\angle 1+35^\circ+60^\circ=180^\circ\\\\\Rightarrow m\angle 1+95^\circ=180^\circ\\\\\Rightarrow m\angle 1=180^\circ-95^\circ\\\\\Rightarrow m\angle 1=85^\circ.[/tex]
Again, since ∠1 and ∠5 makes a linear pair, so
[tex]m\angle 1+m\angle 5=180^\circ\\\\\Rightarrow 85^\circ+m\angle 5=180^\circ\\\\\Rightarrow m\angle 5=180^\circ-85^\circ\\\\\Rightarrow m\angle 5=95^\circ.[/tex]
Thus, the measure of ∠5 is 95°. Option (A) is correct.
