d is your answer
each side of the pentagon is multiplied by 5/3 to get the length of each new side, so the perimeter is multiplied by 5/3 to get the new perimeter.
new perimeter = (scale factor)*(old perimeter)
new perimeter = (5/3)*(old perimeter)
new perimeter = (5/3)*(21)
new perimeter = (5/3)*(21/1)
new perimeter = (5*21)/(3*1)
new perimeter = 105/3
new perimeter = 35 inches
the rule is that for any triangle, the three angles always add to 180 degrees
so a+b+c = 180
replace a with 65, replace b with 3x-10 and replace c with 2x to get this new updated equation: 65 + 3x-10 + 2x = 180
now let's isolate x
65 + 3x - 10 + 2x = 180
5x + 55 = 180 combine like terms
5x + 55 - 55 = 180 - 55 subtract 55 from both sides
5x = 125
5x/5 = 125/5 divide both sides by 5
x = 25
we can stop here since your teacher only wants to know the value of x.
if you're curious how to find the other angles, then replace x with 25 and compute
angle b = 3x - 10 = 3*25 - 10 = 75 - 10 = 65 degrees
angle c = 2*x = 2*25 = 50 degrees
therefore, the three angles of the triangle are a = 65, b = 65, c = 50. as a check, they should add to 180. it turns out they do since a+b+c = 65+65+50 = 130 + 50 = 180. therefore, the answer is confirmed.
note: since angles a and b are both the same at 65 degrees, this means the triangle is isosceles (the sides opposite the congruent angles are congruent sides). we do not have enough info to actually find the length of any of the three sides.
it is 87.5% decrease