Question

ABCDE is a regular pentagon .AB,DC are produced to meet at P .Find angle BPC

Answer 1

hope it helps you ....

Answer 2

Thus, The value of $\angle BPC$ is $36$°

Step-by-step explanation:

Given,

$ABCDE$ is a regular pentagon and $AB,DC$ are produced to meet at $P$ as soon in figure.

We know,

The measure of the interior angle of a regular pentagon is $108$°

∴ From figure,

$\angle ABC=108$° and $\angle BCD=108$°

∴$\angle CBP=180-\angle ABC$

⇒$\angle CBP=(180-108)$

⇒$\angle CBP=72$°

And

$\angle BCP=180-\angle BCD$

⇒$\angle BCP=(180-108)$

⇒$\angle BCP=72$°

From $\triangle BCP$,

$\angle CBP+\angle BCP+\angle BPC=180$

⇒$\angle BPC=180-72-72$

∴$\angle BPC=36$°

So, The value of $\angle BPC$ is $36$°