Answer:
Option B is correct,
The value of \(\angle FOD\) is \(63^{\circ}\)
Explanation:
From the given figure;
\(\angle COB =90^{\circ}\) , \(\angle BOG =15^{\circ}\), and \(\angle GOF=12^{\circ}\).
Linear pair is a pair of adjacent angles formed when two lines intersect. i.e,
\(\angle COB\) and \(\angle BOD\) are linear pairs.
Also, the two angles of linear pair are always supplementary angle[ measure of a straight angle is 180 degrees].
\(\angle COB+\angle BOD=180^{\circ}\)
we can write \(\angle BOD\) as
\(\angle BOD = \angle BOG+\angle GOF+\angle FOD\)
then;
\(\angle COB+\angle BOG+\angle GOF+\angle FOD=180^{\circ}\)
Substitute the given values above to solve for angle FOD;
\(90^{\circ}+15^{\circ}+12^{\circ}+\angle FOD=180^{\circ}\)
or
\(117^{\circ}+\angle FOD=180^{\circ}\)
Simplify:
\(\angle FOD =180-117=63^{\circ}\)
Therefore, the value of \(\angle FOD=63^{\circ}\)
