MATH SOLVE

3 months ago

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

Accepted Solution

A:

Answer:The measure of angle BEA is [tex]110\°[/tex]Step-by-step explanation:we know thatThe measure of the inner angle is the semi-sum of the arcs comprising it and its oppositeso[tex]m<BEA=\frac{1}{2}(arc\ AB+arc\ CD)[/tex]step 1Find the measure of arc ADRemember that the inscribed angle is half that of the arc it comprises.[tex]24\°=\frac{1}{2}(arc\ AD)[/tex][tex]arc\ AD=48\°[/tex]step 2Find the measure of arc BCRemember that the inscribed angle is half that of the arc it comprises.[tex]46\°=\frac{1}{2}(arc\ BC)[/tex][tex]arc\ BC=92\°[/tex]step 3Find the measure of (arc AB + arc CD)[tex]arc\ AB+arc\ CD=360\°-(arc\ AD+arc\ BC)[/tex][tex]arc\ AB+arc\ CD=360\°-(48\°+92\°)[/tex][tex]arc\ AB+arc\ CD=220\°[/tex]step 4Find the measure of angle BEA[tex]m<BEA=\frac{1}{2}(arc\ AB+arc\ CD)[/tex][tex]m<BEA=\frac{1}{2}(220\°)=110\°[/tex]