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In a quad, ABCD, the line segments bisecting angle C and angle D meets at E. Prove that angle A + angle B = 2 angle CED ?

Asked by Vikas 25th February 2016, 10:10 AM
Answered by Expert
Answer:

begin mathsize 14px style I n space t r i a n g l e space C E D comma space w e space h a v e angle C E D plus angle 1 plus angle 2 equals 180 degree rightwards double arrow angle C E D equals 180 degree minus left parenthesis angle 1 plus angle 2 right parenthesis equals 180 degree minus open parentheses 1 half angle C plus 1 half angle D close parentheses equals 180 degree minus 1 half open parentheses angle C plus angle D close parentheses equals 180 degree minus 1 half open square brackets 360 degree minus open parentheses angle A plus angle B close parentheses close square brackets equals 180 degree minus 180 degree plus 1 half open parentheses angle A plus angle B close parentheses rightwards double arrow 2 angle C E D equals angle A plus angle B end style

Answered by Expert 25th February 2016, 6:09 PM
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