Question

In the given figure, AB || CD || EF. If ∠BCE = 35°

and ∠CEF = 135°, then find the measure of

∠ABC.​

Answer 1

angle ABC =80

Step-by-step explanation:

angle CEF +ECD=180

=angle ECD=45

Angle ECD+BCE=angle BCD

=angle BCD=80

angle BCD = angle ABC

ABC = 80

Answer 2

Given:

∠BCE = 35°

and ∠CEF = 135°

To find:

The measure of  ∠ABC.

Solution:

1) Extend the line FE parallel to AB intersects the line BC at O.

2) Then we have a triangle OEC where,

• ∠BCE = 35°

and

• ∠OEC = 180 - ∠CEF
• ∠OEC = 180 - 135
• ∠OEC = 45

and

• ∠ EOC = 180 -∠BCE-∠OEC
• ∠ EOC = 180 -35-45
• ∠ EOC = 180 -80
• ∠ EOC = 100.

now

• ∠ EOB = 180 - 100 ( Linear pair)
• ∠ EOB = 80

3) ∠ EOB = ∠ ABC ( alternate interior angle)

• ∠ ABC = 100

The measure of  ∠ABC is 100°