Question

The diagram shows two congruent regular pentagons and part of a regular n-sided polygon A. Two sides of each of the regular pentagons and two side of A meet at the pint P. Calculate the value of n.​

Answer 1

Answer:

n=10

Step-by-step explanation:

For a regular polygon with n sides, each interior angle, x, is given by

$x=180\frac{n-2}{n}$

This can be solved for n

$n=\frac{360}{180-x}$

For the pentagons

x(5)=180(3/5)=108 degrees.

The angles around P sum to 360, so

2(x(5))+x(A)=360

x(A)=360-2(108)=144.

Substitue in the equation for n.

n=360/(180-144)=10