Answer:
75
Step-by-step explanation:
angle 2 and angle 6 are corresponding angles, because the lines are parallel and cut by a transversal, corresponding angles are congruent, thus if angle 2 is 75 degrees then angle 6 is 75 degrees
Check the picture below.
let's notice that the base of the pyramid is triangle with a base of 5 and an altitude of 4, so it has an area of (1/2)(5)(4).
![\bf \textit{volume of a pyramid}\\\\ V=\cfrac{1}{3}Bh~~ \begin{cases} B=\stackrel{\textit{area of its}}{base}\\ h=height\\[-0.5em] \hrulefill\\ B=\frac{1}{2}(5)(4)\\ h=8 \end{cases}\implies V=\cfrac{1}{3}\left( \cfrac{1}{2}(5)(4) \right)(8)\implies V=\cfrac{1}{3}(10)(8) \\\\\\ V=\cfrac{80}{3}\implies V=26\frac{2}{3}](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Bvolume%20of%20a%20pyramid%7D%5C%5C%5C%5C%20V%3D%5Ccfrac%7B1%7D%7B3%7DBh~~%20%5Cbegin%7Bcases%7D%20B%3D%5Cstackrel%7B%5Ctextit%7Barea%20of%20its%7D%7D%7Bbase%7D%5C%5C%20h%3Dheight%5C%5C%5B-0.5em%5D%20%5Chrulefill%5C%5C%20B%3D%5Cfrac%7B1%7D%7B2%7D%285%29%284%29%5C%5C%20h%3D8%20%5Cend%7Bcases%7D%5Cimplies%20V%3D%5Ccfrac%7B1%7D%7B3%7D%5Cleft%28%20%5Ccfrac%7B1%7D%7B2%7D%285%29%284%29%20%5Cright%29%288%29%5Cimplies%20V%3D%5Ccfrac%7B1%7D%7B3%7D%2810%29%288%29%20%5C%5C%5C%5C%5C%5C%20V%3D%5Ccfrac%7B80%7D%7B3%7D%5Cimplies%20V%3D26%5Cfrac%7B2%7D%7B3%7D)
Answer:
18 cm for larger base
Step-by-step explanation:
For similar figures, there is a formula regarding volume, area, and length
Large: small = y: x for length
large: small = (y^3) / (x^3) for volume
729 cm cube/ 64 cm cube = large : small
9: 4 = large: small by length
large/ 8cm = 9/ 4
large = 8*(9/4) = 2*9 = 18 cm