Question

Given: circle k(O), DC ∥ AB , AC ∩ DB =0, m AD =124°Find: m∠C, m∠AOB.

Answer 1

Part 1) The measure of angle C is
`62\°`

Part 2) The measure of angle AOB is
`56\°`

Explanation:

step 1

Find the measure of angle C

we know that

The inscribed angle measures half that of the arc comprising

so

`m<C=(1)/(2)(arc\ AD)`

we have

`arc\ AD=124\°`

substitute

`m<C=(1)/(2)(124\°)=62\°`

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°