Answer:
x = 44°
Step-by-step explanation:
The sum of the three angles is 180°.
So, x + x + 5 + 2x -1 = 180
4x + 4 = 180
4x = 176
x = 44°
Ok so 24 of them and that would be ur answer
Answer:
(b) 1.7 in
Step-by-step explanation:
The area of a regular polygon in terms of perimeter and apothem is given by the formula ...
A = 1/2Pa
For a hexagon, the perimeter is 6 times the side length, so this becomes ...
A = 1/2(6s)a = 3sa . . . . . for side length 's' and apothem 'a'
__
Solving for the apothem, we find ...
a = A/(3s)
For the given values of area and side length the apothem is ...
a = 10.4/(3·2) = 1.733... ≈ 1.7 . . . inches
The apothem, rounded to tenths, is 1.7 inches.
-- You have two angles.
-- They're complementary . . . they add up to 90 degrees.
-- One is 4 times as big as the other one.
___________________________________________
-- The smaller angle has 1 share of the 90 degrees.
-- The bigger angle has 4 shares of the 90 degrees.
-- (The smaller one is 1/4 the size of the bigger one.
The bigger one is 4 times the size of the smaller one.)
-- When you add them together, you get 5 shares, totaling 90 degrees.
-- What's the size of each share ? It's 90/5 = 18 degrees.
-- The smaller angle gets one share . . . 18 degrees.
-- The bigger angle gets 4 shares. (4 x 18) = 72 degrees.
____________________________________
Check:
-- Is the small one 1/4 the size of the big one ? 18/72 = 1/4 Yes.
-- Are they complementary ? Do they add up to 90 degrees ?
18 + 72 = 90 Yes.
yay !
Length: 2w + 59
width: w
diagonal: (2w + 59) + 2 = 2w + 61
Length² + width² = diagonal²
(2w + 59)² + (w)² = (2w + 61)²
(4w² + 118w + 3481) + w² = 4w² + 122w + 3721
5w² + 118w + 3481 = 4w² + 122w + 3721
w² + 118w + 3481 = 122w + 3721
w² - 4w + 3481 = 3721
w² - 4w - 240 = 0
a = 1, b = -4, c = -240
w = ![[-(b) +/- \sqrt{(b)^{2} - 4(a)(c) }]/2(a)](https://tex.z-dn.net/?f=%5B-%28b%29%20%2B%2F-%20%5Csqrt%7B%28b%29%5E%7B2%7D%20%20-%204%28a%29%28c%29%20%7D%5D%2F2%28a%29)
= ![[-(-4) +/- \sqrt{(-4)^{2} - 4(1)(-240) }]/2(1)](https://tex.z-dn.net/?f=%5B-%28-4%29%20%2B%2F-%20%5Csqrt%7B%28-4%29%5E%7B2%7D%20%20-%204%281%29%28-240%29%20%7D%5D%2F2%281%29)
= ![[4 +/- \sqrt{(16 + 960) }]/2](https://tex.z-dn.net/?f=%5B4%20%2B%2F-%20%5Csqrt%7B%2816%20%20%2B%20960%29%20%7D%5D%2F2)
= ![[4 +/- \sqrt{(976) }]/2](https://tex.z-dn.net/?f=%5B4%20%2B%2F-%20%5Csqrt%7B%28976%29%20%7D%5D%2F2)
= ![[2 +/- 4\sqrt{(61) }]/2](https://tex.z-dn.net/?f=%5B2%20%2B%2F-%204%5Csqrt%7B%2861%29%20%7D%5D%2F2)
= 
since width cannot be negative, disregard 1 - 2√61
w = 1 + 2√61 ≈ 16.62
Length: 2w + 59 = 2(1 + 2√61) + 59 = 2 + 4√61 + 59 = 61 + 4√61 ≈ 92.24
Answer: width = 16.62 in, length = 92.24 in
