Answer:
119
Step-by-step explanation:
By using exterior angle theorem, we know that 31+angle 1 =150. therefore angle 1=119. Exterior angle theorem is where an angle exterior of an angle in the triangle addus up to 180 degreees, we also know the angles in a triangle sum to 180 degrees. Both sides have a common angle. If we subract it from the equation, we get what is said above.
Answer:
cylinder
Step-by-step explanation:
Answer: the number of adult tickets is 210
The number if student tickets is 270
Step-by-step explanation:
Let x represent the number of adult tickets that were purchased.
Let y represent the number of student tickets that were purchased.
At the ritz, concert tickets for adults cost $6 and tickets for students cost $4. If the cost of total tickets purchased is $2340, then,
6x + 4y = 2340 - - - - - - - -1
Total number of tickets purchased is 480. This means that
x + y = 480
x = 480 - y
Substituting x = 480 - y into equation 1, it becomes
6(480 - y) + 4y = 2340
2880 - 6y + 4y = 2340
- 6y + 4y = 2340 - 2880
-2y = - 540
y = - 540/-2 = 270
x = 480 - 270
x = 210
Check the picture below.
let's recall that in a Kite, the diagonals meet at 90° angles, therefore, we know the height of each of those 4 triangles, is 2.5 and 6, now, since the pair of triangles above are 45-45-90 triangles, we can use the 45-45-90 rule, as you see there, so, if the height is 2.5, then the base is also 2.5.
so, we really have 2 pair of triangles whose base is 2.5 and height of 2.5, and another pair of triangles whose base is 2.5 and height is 6, let's add their areas.
![\bf \stackrel{\textit{area of 2 triangles above}}{2\left[\cfrac{1}{2}(2.5)(2.5) \right]}~~+~~\stackrel{\textit{area of 2 triangles below}}{2\left[ \cfrac{1}{2}(2.5)(6) \right]}\implies 6.25+15\implies 21.25](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7B%5Ctextit%7Barea%20of%202%20triangles%20above%7D%7D%7B2%5Cleft%5B%5Ccfrac%7B1%7D%7B2%7D%282.5%29%282.5%29%20%5Cright%5D%7D~~%2B~~%5Cstackrel%7B%5Ctextit%7Barea%20of%202%20triangles%20below%7D%7D%7B2%5Cleft%5B%20%5Ccfrac%7B1%7D%7B2%7D%282.5%29%286%29%20%5Cright%5D%7D%5Cimplies%206.25%2B15%5Cimplies%2021.25)
