ABCD is a trep. with AB//DC and AD = BC. If AD is parallel to CE and angle A is 70 degrees.Find all the angles ? Diagram is given below.

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Answer 1 · 2017-02-07T06:34:00

See explanation.

Given:

(1) trapezoid #ABCD#
(2) #bar(AB) " || " bar(CD)#
(3) #bar(AD) ~= bar(BC)#
(4) #bar(AD) " || " bar(CE)#
(5) #"m"angleA=70°#

We can immediately obtain

(6) #"m"angle D = 110°#

because #angle A# and #angle D# are co-interior angles, thus their sum is #180°#.

(2) & (4) tell us that

(7) #AECD# is a parallelogram

and thus

(8) #bar(AD) ~= bar(EC)#

From (3) and (8) we get

(9) #bar(BC) ~=bar(EC)#
(10) #triangleECB ~= triangle BCE#

and so

(11) #angle CEB ~= angle B#

From (4), we get

(12) #angle A ~= angle CEB#

This, together with (11) gives

(13) #angle A ~= angle B#
(14) #"m"angle B =70°#

Just as #angle A# and #angle D# are co-interior angles, #angle B# and #angle BCD# are co-interior angles, so

(15) #"m"angle BCD =110°#.

From (11) and (14), we get

(16) #"m"angle CEB = 70°#

and since #angle AEC# and #angle CEB# are supplementary,

(17) #"m"angle AEC = 110°#

#angle AEC# and #angle ECD# are co-interior, so

(18) #"m"angle ECD = 70°#

Finally, we use (15) and (18) to get

(19) #"m"angle BCE = 40°#.