Answer:
[tex]m\angle 2=58^o[/tex]
Step-by-step explanation:
see the attached figure with letters to better understand the problem
step 1
Find the measure of arc BC
we know that
[tex]arc\ AB+arc\ BC+arc\ AC=360^o[/tex] ----> by complete circle
substitute the given values
[tex]156^o+arc\ BC+88^o=360^o[/tex]
[tex]244^o+arc\ BC=360^o[/tex]
[tex]arc\ BC=360^o-244^o=116^o[/tex]
step 2
Find the measure of angle 2
we know that
The inscribed angle is half that of the arc it comprises.
so
[tex]m\angle 2=\frac{1}{2}[arc\ BC][/tex]
substitute
[tex]m\angle 2=\frac{1}{2}[116^o]=58^o[/tex]
