Question

The diagram shows a regular octagon joined to an equilateral triangle work out the value of X

Answer 1

Answer:

$x=165^o$

Step-by-step explanation:

we know that

The measure of the interior angle in an equilateral triangle is equal to 60 degrees

The measure of the interior angle in a regular octagon is equal to

$\frac{(n-2)180}{n}$

where

n is the number of sides

In this problem we have

$n=8\ sides$

substitute

$\frac{(8-2)180}{8}$

$\frac{(6)180}{8}=135^o$

we have that, based in the diagram

The sum of the interior angle of the equilateral triangle plus the interior angle of a regular octagon plus the value of x must be equal to 360 degrees (complete circle)

so

$x+60^o+135^o=360^o$

solve for x

$x+195^o=360^o$

$x=360^o-195^o$

$x=165^o$