Answer: The answer is (D) \(132^\circ.\)
Step-by-step explanation: We are given a figure where the line segments AE and RV are intersecting at the point N. We are to find the measure of \(\angle ENV.\)
Also, given that
\(\angle ANR=(8x+12)^\circ,\\\\\angle ENV=(5x+57)^\circ.\)
Since the line segments AE and RV intersect at N, so we have
\(\angle ANR=\angleENV~[\textup{vertically opposite angles}]\\\\5x+57=8x+12\\\\\Rightarrow8x-5x=57-12\\\\\Rightarrow3x=45\\\\\Rightarrow x=15.\)
Therefore,
\(\angle ENV=(5\times 15+57)^\circ=(75+57)^\circ=132^\circ.\)
Thus, (D) is the correct option.
