Question

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

Answer 1

Answer:

The measure of angle BEA is $110\°$

Step-by-step explanation:

we know that

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

so

$m<BEA=\frac{1}{2}(arc\ AB+arc\ CD)$

step 1

Find the measure of arc AD

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

$24\°=\frac{1}{2}(arc\ AD)$

$arc\ AD=48\°$

step 2

Find the measure of arc BC

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

$46\°=\frac{1}{2}(arc\ BC)$

$arc\ BC=92\°$

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

$m<BEA=\frac{1}{2}(arc\ AB+arc\ CD)$

$m<BEA=\frac{1}{2}(220\°)=110\°$