Answer: AD = 108
BD = 105
ADB = 213
ABC = 182
Step-by-step explanation:
If no radius is given, assume it is length 1.
Then, the length of the arc is equal to the central angle.
Reminder that a circle is 360°
[tex]\bold{\underline{\stackrel\frown{AD}:}}[/tex]
The central angle = 108°, so the arc length = 108
[tex]\bold{\underline{\stackrel\frown{BD}:}}[/tex]
BD = BC + CD
= 35° + 70°
= 105°
The central angle = 105°, so the arc length = 105
[tex]\bold{\underline{\stackrel\frown{ADB}:}}[/tex]
ADB = AD + CD + BC
= 108° + 70° + 35°
= 213°
The central angle = 213°, so the arc length = 213
[tex]\bold{\underline{\stackrel\frown{ABC}:}}[/tex]
First, find the angle of AB.
AB = 360° - ADB
= 360° - 213°
= 147°
ABC = AB + BC
= 147° + 35°
= 182°
The central angle = 182°, so the arc length = 182
