Help again?

Question

693 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-05-22T17:37:27

#angle AED = 1/2( 62^circ + 28^circ)=45^circ#

These are intersecting chords, and there's a theorem about their angles I can't remember. Let's derive it.

The angle subtended by a chord is half the central angle from the radius to the chord endpoints, which is the arc measure.

#angle ABD = 1/2 text{arc}(AD)#

#angle BAC = 1/2 text{arc}(BC)#

#angle ABD + angle BAC + angle AEB = 180^circ #

#angle AED = 180^circ - angle AEB = angle ABD + angle BAC #

#angle AED = 1/ 2(text{arc}(AD ) + text{arc}(BC) )#

#angle AED = 1/2( 62^circ + 28^circ)=45^circ#