Question

in the figure show that AB is parallel to EF ​

Answer 1

Step-by-step explanation:

Given,

<ABC = 66° , < BCE = 36° & <ECD = 30° .

As we know ,

<BCD = <BCE + <ECD

<BCD = (36+30)°

<BCD = 66° .

We know that corresponding angle are equal in parallel lines. Here , <ABC = 66° and <BCD = 66° (both of them are equal according to corresponding angle )

Thus, AB||CD .

Now, Given, <CEF = 150°a d <ECD = 30° .

we know that , sum of interior angles in parrallel lines are equal to 180° .

Here ,

Sum of interior angles = <CEF + <ECD = 180°

150°+30° = 180°

180° = 180° .

the sum is equal to 180° , thus , CD || EF .

Now, Here , As we know according to the question , the overall results is

AB || CD || EF .

From, the above statement, it can be concluded that AB || EF .

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Answer 2

Answer:

Given:Angle ABC=66°

angle BCE=36°

angle ECD= 30°

Now, angle BCE+ECD= 36°+30°

=66°= angle BCD

therefore angle ABC= angle BCD=66°

So,AB||CD[when alternate interior angles are equal then lines are parallel]

Now angle FEC + angle ECD

150°+30°=180°

so,CD||EF[when the sum of interior angle of the same side of transversal is 180°then lines are parallel]

so,AB||CD

CD||EF

therefore AB||EF [if two sides are parallel to the same sides then they are parallel to one another]