Question

If $ABCDE$ is a regular pentagon, show that $AB$ is parallel to $EC$.

Answer 1

Five sided pentagon is called regular pentagon

We know that all angle of regular pentagon is 108

In triangle CD=DE (All sides ofregular pentagon is equal)

Then angle ECD =angle DEC=x (let)

In triangle ECD

x+x+108=180

Or 2x=72 or x=36

Then angle ECD=angle DEC=36

So angle ECB=108-36=72

And angle CBA=108

Then angle ECB+angle CBA=72+108=180

Similarly we can have

angle CEA+angle Bae=180

As sum of adjacent angle are 180

Then AB II EC