Question

Find the measure of angle 2.

Answer 1

`m\angle 2=58^o`

Explanation:

see the attached figure with letters to better understand the problem

step 1

Find the measure of arc BC

we know that

`arc\ AB+arc\ BC+arc\ AC=360^o` ----> by complete circle

substitute the given values

`156^o+arc\ BC+88^o=360^o`

`244^o+arc\ BC=360^o`

`arc\ BC=360^o-244^o=116^o`

step 2

Find the measure of angle 2

we know that

The inscribed angle is half that of the arc it comprises.

so

`m\angle 2=(1)/(2)[arc\ BC]`

substitute

`m\angle 2=(1)/(2)[116^o]=58^o`