Question

Find the measure of angle 2.

Answer 1

Answer:

$m\angle 2=58^o$

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

$arc\ AB+arc\ BC+arc\ AC=360^o$ ----> 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

$m\angle 2=\frac{1}{2}[arc\ BC]$

substitute

$m\angle 2=\frac{1}{2}[116^o]=58^o$