Question

Question 1: Campsite #1, lookout tower, and campsite #2 form a central angle within the circle. If the angle formed is 120°, describe the relationship between the angle and the arc it intercepts. You must show all work to receive credit. I just need a little help starting this.

Answer 1

1. By Formula 1, m∠CAB = arcBC.
The relationship between the central angle and the arc it intercepts is that they are equal. Since m∠CAB = 120°, then arcBC = 120°.

2. By Formula 2,
m∠ACB = 1/2 • intercepted arc

The relationship is m∠ACB is half of its intercepted arc. If m∠ACB is 30°, then its intercepted arc is 60°.

3. It's saying m∠EDF can be no more than 65° for them to get good signal.

arcEBF + arcECF = 360°
arcEBF + 110° = 360°
arcEBF = 250°

By Formula 5: Two Tangents,
m∠EDF = 1/2 • (arcEFB - arcECF)
m∠EDF = 1/2 • (250° - 110°)
m∠EDF = 70°

Since 70° > 65°, they'll have trouble communicating.

For the second question, draw a line connecting E to F.

By Formula 3,
m∠FED = 1/2 • arcECF    and    m∠EFD = 1/2 • arcECF

Thus,
m∠FED = m∠EFD

Triangle EFD has two equal angles, m∠FED and m∠EFD, making it an isosceles triangle. We can conclude that ED = FD.

Answer 2

Both of their endpoints connect at point A. which is also known as a center angle. this being said the arc must also be 120 degrees. is this right?

Answer 3

yes

Answer 4

okay thanks i just needed help starting it :)