Geometry: Find F?

[saab323]

So ABCD is one straight line. D connects to E and E connects to B, which makes BED a triangle. Then A connects to F and F connects to C, which makes AFC a triangle. A = 63 B= 147 E = 90. Find F? (F ISNT 90.)

 

[HallsofIvy]

So ABCD is one straight line. D connects to E and E connects to B, which makes BED a triangle. Then A connects to F and F connects to C, which makes AFC a triangle. A = 63 B= 147 E = 90. Find F? (F ISNT 90.)

There isn't enough information. Imagine constructing that whole thing out of wire with a loop at C attaching line FC to ABCD. Sliding point C along ABCD changes angle F while not changing any of the given information.

Oops, that does change angle A.

 

[saab323]

There isn't enough information. Imagine constructing that whole thing out of wire with a loop at C attaching line FC to ABCD. Sliding point C along ABCD changes angle F while not changing any of the given information.

Does the picture not help? :O

 

[HallsofIvy]

Well, it does help me see that what I said about angle F not changing as you move point C along the line! But you are given, really, only that angle A is 63 degrees. Given that, we can only say that the measures of angle F and angle C must add to 180- 63= 117 degrees. So F, individually, can be anything above 0 and less then 117. I don't see that triangle BED contributes anything to this.

 

[saab323]

Well, it does help me see that what I said about angle F not changing as you move point C along the line! But you are given, really, only that angle A is 63 degrees. Given that, we can only say that the measures of angle F and angle C must add to 180- 63= 117 degrees. So F, individually, can be anything above 0 and less then 117. I don't see that triangle BED contributes anything to this.

Hmm... doesn't really help, but thanks anyways.

 

[stapel]

Hmm... doesn't really help, but thanks anyways.

Actually, yes, the volunteer's lengthy explanations do help. Have you read them? He explains that you have not been given enough information, explains how you can "see" this, and thus suggests that you need to get more information.

So take this exercise to the instructor who assigned it, and as for clarification. Thank you!

 

[Ishuda]

There isn't enough information. Imagine constructing that whole thing out of wire with a loop at C attaching line FC to ABCD. Sliding point C along ABCD changes angle F while not changing any of the given information.

Oops, that does change angle A.

No. It changes \(\displaystyle \angle\)ACF and \(\displaystyle \angle\)AFC [angle F] and the length of FC but the relationship
\(\displaystyle \angle\)ACF + \(\displaystyle \angle\)AFC = 117
remains.

EDIT: Or move point F along line AF [toward or away from point A] so that the \(\displaystyle \angle\)ACF, \(\displaystyle \angle\)AFC [angle F], the length of FC, and the length of FA change.