How do you find the angle of FAC when:

Question

D is in the interior of <BAE
E is in the interior of <DAE
F is in the interior of <EAC
m<BAC=130 degrees
m<EAC=100 degrees
m<BAD=m<EAF=m<FAC
?

FAC is 40 degrees. All of these lines are linear pairs held on an 180 degree line. If BAD, EAF and FAC are all equal then they are congruent. So since EAC is supplementary to FAC then you are trying to find the measurement of FAC by saying 180-100 gives me what? That answer is 80 degress. But you are not done because you have two more angles on this 180 degree line that is congruent which is EAF and FAC. So if they are congruent, you divide 80 by 2 to give you 40 degrees.
I know sound confusing.

Answer 1

To clarify:

1. BAD, EAF, and FAC are all congruent angles.
2. The sum of EAC and FAC is 180 degrees because they are supplementary.
3. The sum of BAD, EAF, and FAC is also 180 degrees because they form a straight line.

Now, let's use this information to find the measure of angle FAC.

Since EAC is 100 degrees and it is supplementary to FAC, we know that FAC must be 180 - 100 = 80 degrees.

However, we also know that BAD and EAF have the same measure as FAC. Since all three angles are congruent and their sum is 180 degrees, we can divide 80 degrees by the 2 remaining angles:

80 degrees / 2 = 40 degrees

Thus, the measure of angle FAC is 40 degrees.