Question

What is the size of the obtuse angle CBA

Answer 1

`m<CBA=102\°`

Explanation:

we know that

The internal angle of an equilateral triangle is equal to
`60\°`

The internal angle of a square is equal to
`90\°`

To find the internal angle of a regular pentagon, apply the formula

`S=[(n-2)180\°]/n`

where

n is the number of sides (n=5)

substitute

`S=[(5-2)180\°]/5=108\°`

therefore

In this problem

`m<CBA+60\°+90\°+108\°=360\°`

`m<CBA+258\°=360\°`

`m<CBA=360\°-258\°=102\°`