Answer:
x = 9
m(AD) = 108°
m(BC) = 23°
m(DC) = 139°
m(DBC) = 162°
Explanation:
AD = 12x°
BC = (2x + 5)°
DC = (17x - 14)°
m<AEB = right angle = 90°
AB = m<AEB = 90° (central angle theorem)
90 + 12x + (2x + 5) + (17x - 14) = 360 (full circle)
✔️Solve for x
90 + 12x + 2x + 5 + 17x - 14 = 360
Add like terms
81 + 31x = 360
31x = 360 - 81
31x = 279
x = 279/31
x = 9
✔️Find m(AD)
m(AD) = 12x
Plug in the value of x
m(AD) = 12(9) = 108°
✔️Find m(BC):
m(BC) = (2x + 5) = 2(9) + 5
m(BC) = 23°
✔️Find m(DC) = (17x - 14)° = 17(9) - 14
m(DC) = 139°
✔️Find m(DBC) = m(DC) + m(BC) = 139° + 23° = 162°