Question

can u help with the bonus

Answer 1

The sum of the interior and exterior angle need to equal 180 degrees.

Let the exterior angle = X

You are told the interior angle = 38x +24

Now you have x + 38x +24 = 180

Combine like terms:

39x +24 = 180

Subtract 24 from each side:

39x = 156

Divide both sides by 39:

x = 156 / 39

x = 4

The number of sides is found by dividing 360 by the exterior angle:

360 / 4 = 90

There are 90 sides.

Answer 2

Any exterior angle is supplementary to any interior angle, so the sum of their measures is 180 degrees. If $x$ is the measure of one of these interior angles, then $180-x$ is the measure of the corresponding exterior angle.

We're told that

$x=24+38(180-x)$

Solve for $x$:

$x=24+6840-38x\implies 39x=6864\implies x=176$

which means the exterior angles each have measure 180 - 176 = 4 degrees.

In a regular polygon with $n$ sides, the sum of the measures of all the exterior angles is 360 degrees:

$360=4n\implies n=\dfrac{360}4=90$

so this polygon has 90 sides.