Question

Use this figure to find the value of ∠FOD.

A. 27°
B. 63°
C. 46°
D. 78°

Answer 1

m<FOD = 90 -12 -15

m<FOD = 63

answer is B. 63

hope it helps

Answer 2

Option B is correct,

The value of
`\angle FOD` is
`63^(\circ)`

Step-by-step 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)`