Question

If m∠B = 24°, and m∠D = 46°, what is m∠BEA?

Answer 1

The measure of angle BEA is
`110\°`

Explanation:

we know that

The measure of the inner angle is the semi-sum of the arcs comprising it and its opposite

so

`m<BEA=(1)/(2)(arc\ AB+arc\ CD)`

step 1

Find the measure of arc AD

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

`24\°=(1)/(2)(arc\ AD)`

`arc\ AD=48\°`

step 2

Find the measure of arc BC

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

`46\°=(1)/(2)(arc\ BC)`

`arc\ BC=92\°`

step 3

Find the measure of (arc AB + arc CD)

`arc\ AB+arc\ CD=360\°-(arc\ AD+arc\ BC)`

`arc\ AB+arc\ CD=360\°-(48\°+92\°)`

`arc\ AB+arc\ CD=220\°`

step 4

Find the measure of angle BEA

`m<BEA=(1)/(2)(arc\ AB+arc\ CD)`

`m<BEA=(1)/(2)(220\°)=110\°`