Question

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

Answer 1

`x=165^o`

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

`((n-2)180)/(n)`

where

n is the number of sides

In this problem we have

`n=8\ sides`

substitute

`((8-2)180)/(8)`

`((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`