Question

Find the value of m

Answer 1

Option C. 32°

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°