Answer:
Option C. 32°
Step-by-step explanation:
see the attached figure with letters to better understand the problem
step 1
Find the measure of arc AB
we know that
The semi-inscribed angle measures half that of the arc comprising
so
74°=(1/2)[arc AB]
arc AB=(2)(74°)=148°
step 2
Find the measure of arc BCDA
we know that
arc BCDA+arc AB=360°
substitute the given value
arc BCDA+148°=360°
arc BCDA=360°-148°=212°
step 3
find the measure of angle m
we know that
The measurement of the outer angle is the semi-difference of the arcs it encompasses.
so
m=(1/2)[arc BCDA-arc AB]
substitute
m=(1/2)[212°-148°]=32°
