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

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 $\angle FOD=63^{\circ}$