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In the diagram below, BA and BC are tangents to the circle at points A and CC respectively. If angle AEC = 110 degrees and angle DCE = 80 degrees, find angle ABC.

 

 May 13, 2020
 #1
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Note  that arc ADC  =  2*measure of angle AEC =  2*110  = 220°

 

So  angle ADC  intercepts  arc AEC =  360 - 220  = 140°

 

So  we have this relationship : 

 

x = (1/2) (arc ADC - arc AEC)  =  (1/2) ( 220 - 140) =  (1/2)(80)  = 40° 

 

 

cool cool cool

 May 13, 2020

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