Line AB and CD intersect at E. If angle AEC = #4x - 40# and angle BED = #x+50#, what is the number of degrees in AEC?

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Answer 1 · 2017-09-26T14:13:09

Angle #AEC=80#

Angle AEC = Angle BED as they are vertically opposite angles.
#:.4x-40=x+50#
#4x-x=50+40#
#3x=90#
#x=30#
Angle #AEC=4x-40=(4*30)-40=120-40=80#

Answer 2 · 2017-09-26T14:39:39

#/_ AEC = 80^@#

Given:
#/_ AEC = 4x -40#
#/_ BED = x+ 50#

# /_ AEC = /_ BED #----------as they are vertically opposite angles. i.e. they share the same vertex.
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Therefore:

#4x - 40 = x + 50#

Bring terms with variable x on one side and take rest on other side (apply rules of transposition):

#4x -x = 50 + 40#

#3x = 90#

# x = 30#

Therefore

#/_ AEC = 4x - 40# = #4\times 30 -40#

#/_ AEC = 120 -40#

#/_ AEC = 80^@#