Question

please answer this with solution !

1.)find the measure of an angle whose supplement is three times its complement.
2.)triangle ABC is similar to triangle XYZ. what is the length of segment XZ if BC=9m, AC=6m, and YZ=3m?
3.)a square with the side w is drawn inside a 6 unit square.what equation represents the area of the 6 unit square excluding the area of the square inside it?
4.)the perimeter of regular triangle, regular pentagon, regular hexagon, and regular octagon are respectively equal to 57 cm, 70 cm, 105 cm, and 112 cm.which figure have sides with the longest measure?

Answer 1

1)
let the angle be x
so the supplement is (180-x)
so the complement is (90-x)
since the supplement is 3 times the complement, we have
(180-x)=3(90-x)
180-x=270-3x
2x=90
x=45

Answer 2

2)
if the triangles are similar, then this means ONE thing.
that is, there sides are in proportion. furthermore, the CORRESPONDING sides of both triangles differ by some constant number
that means
XZ/AC = YZ/BC
XZ = AC(YZ/BC)
make your substitutions
XZ = 6(3/9)
XZ = 2

Answer 3

3) area of the 6 unit square is 6x6 = 36
area of the smaller square is wxw
now, let the area of what we're trying to find be A
hence a sensible equation is
A = 36-w^2

Answer 4

4)
regular means, all sides are equal
so , for:
triangle, sides = 57/3 = 19
pentagon, sides = 70/5 = 14
hexagon, sides = 105/7 = 15
octagon, sides = 112/8 = 14
so the hexagon has the sides with the longest measure.