Answers and Step-by-step explanation:
1. (a) First off, we know that arc BFE is 180 degrees because it's a semicircle. That means that arc FE + arc BF = 180, and since arc BF = 135, then arc FE = 180 - 135 = 45 degrees. Now, arc FD is just arc FE + arc ED, so 45 + 81 = 126 degrees.
(b) Arc BD is just the whole circle (360 degrees) minus arc BFD. From part A, we know that arc BFD = 135 + 45 + 81 = 261 degrees. So, arc BD = 360 - 261 = 99 degrees.
(c) Arc FBC is just 180 degrees because it's a semicircle.
(d) Arc CD = arc FDC - arc FD = 180 - (45 + 81) = 54 degrees. Arc FBD = arc FBC + arc CD = 180 + 54 = 234 degrees.
2. You can use similar reasoning to figure out these arc measures; I'm just going to provide the answers.
(a) 126 degrees
(b) 117 degrees
(c) 234 degrees
(d) 297 degrees
3. (a) 180 degrees
(b) 180 - 55 = 125 degrees
(c) 360 - 55 = 305 degrees
(d) 180 + 55 = 235 degrees
Hope this helps!
