a = 29°
c = 40°
b = 61°
Step-by-step explanation:
The intercepted arc = 2 × inscribed arc
The intercepted arc = 58°
inscribed arc = a°
58° = 2(a°)
58 = 2a
a = 58/2
a = 29°
The intercepted arc = 80°
inscribed arc = c°
80 = 2(c°)
80 = 2c
c = 80/2
c = 40°
58° + the unknown arc = 180° (angle on a straight line)
the unknown arc = arc after 58 degrees towards m
the unknown arc = 180° - 58°
the unknown arc = 122°
b = 1/2(unknown arc)
b = 1/2(122)
b = 61°