Answer:
Part 1) The measure of angle C is [tex]62\°[/tex]
Part 2) The measure of angle AOB is [tex]56\°[/tex]
Step-by-step explanation:
step 1
Find the measure of angle C
we know that
The inscribed angle measures half that of the arc comprising
so
[tex]m<C=\frac{1}{2}(arc\ AD)[/tex]
we have
[tex]arc\ AD=124\°[/tex]
substitute
[tex]m<C=\frac{1}{2}(124\°)=62\°[/tex]
step 2
Find the measure of angle AOB
we know that
In the isosceles triangle ODC
∠D=∠C=62°
Remember that
The sum of the internal angles of a triangle must be equal to 180 degrees
so
∠D+∠C+∠DOC=180°
substitute the values
62°+62°+∠DOC=180°
∠DOC=180°-124°=56°
we have that
∠AOB=∠DOC -----> by vertical angles
so
∠AOB=56°
