Question

The interior angles of a quadrilateral are 2x+15 2x-5 3x+75 3x-25 find x and the smallest interior angle largest interior angle and smallest exterior angle

Answer 1

Answer:
`x=30^(\circ)`

Explanation:

We know sum of the interior angles of a quadrilateral is
`360^(\circ)`

therefore we can write

`(2x+15)+(2x-5)+(3x+75)+(3x-25)=360^(\circ)`

so

`\Rightarrow 10x+60=360`

`\Rightarrow 10x=300`

`\Rightarrow x=30^(\circ)`

So smallest interior angle is
`(2x-5)^(\circ)=(60-5)=55^(\circ)`

Largest interior angle
`=3x+75=90+75=165^(\circ)`