# 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.

##### 1 Answer

See explanation.

#### 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

(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

(15)

#"m"angle BCD =110°# .

From (11) and (14), we get

(16)

#"m"angle CEB = 70°#

and since

(17)

#"m"angle AEC = 110°#

(18)

#"m"angle ECD = 70°#

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

(19)

#"m"angle BCE = 40°# .