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