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

Question

asked Mar 14, 2021 119k views

1 Answer

Marc Gear · Answer 1 · 2021-03-20T02:05:09+0000

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
$=3x+75=90+75=165^(\circ)$