can someone please answer these questions for me?:

Question

1. if the measure of an interior angle of a regular pentagonis 108 degrees, then the angle sum of that regular pentagon must be:
A. 120 degrees
B. 360 degrees
C. 540 degrees
D. 720 degrees

2. is it possible for a parallelogram to have a 38 degree angle and a 145 degree angle? explain please

3. a rectangle has a perimeter of 24 centimeters. one of its sides is 8 centimeters long. what are the dimensions of the rectangle? explain please

4. is it possible for a triangle to have angles with measures of 40 degrees, 115 degrees and 30 degrees? please explain

thanks :D sorry if theres soo many questions, i just really need help

Answer 1

sum of interior angles = 180(n-2) where n is the number of sides
so each angle is 180(n-2)/n

180(n-2)/n = 108
180n - 360 = 108n
72n = 360
n = 5

So you have a pentagon
angle sum = 180(5-2) = 540

do the others the same way.
Remember in #2, that n has to be a whole number.
(e.g. A pentagon cannot have 4.3 sides)

#3. Just think about it again.
you have one of the sides.
How does one find the perimeter?

Answer 2

You add it up