Question

In the figure abcde is a regular pentagon. Find <BPC?

​

Answer 1

Step-by-step explanation:

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

We know,

The measure of the interior angle of a regular pentagon is 108108 °

∴ From figure,

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

∴\angle CBP=180-\angle ABC∠CBP=180−∠ABC

⇒\angle CBP=(180-108)∠CBP=(180−108)

⇒\angle CBP=72∠CBP=72 °

And

\angle BCP=180-\angle BCD∠BCP=180−∠BCD

⇒\angle BCP=(180-108)∠BCP=(180−108)

⇒\angle BCP=72∠BCP=72 °

From \triangle BCP△BCP ,

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

⇒\angle BPC=180-72-72∠BPC=180−72−72

∴\angle BPC=36∠BPC=36 °

So, The value of \angle BPC∠BPC is 3636