Solve for x and y in the diagrams below.

1. x = 13, y = 11.5

2. x = 39, y = 123

Step-By-Step Explanation: For the first diagram, you can see that 10x - 42 = 6x + 10 by way of vertical angles. Vertical angles are two opposite angles created by the same two lines, meaning that they will ALWAYS be congruent. Solving for x, you get that 4x = 52, or that x = 13. There is another thing. Both of the diagrams have a total angle measurement of 360, since they both go all the way around. Knowing that, 6x + 10 + 8y must be equal to half of that, or 180. Solving for 88 + 8y = 180 (since you know the value of x), you know that 8y = 92, or x = 11.5.

For number two, the concept is very similar, but this time there's more angles. You can immediately see that there are 3 pairs of vertical angles. The value of the angle squishes between the x - 10 and the 3x + 6 is x - 11; again, vertical angles. The angle squished between 3x + 6 and x - 11 is x - 10 (vertical angles!). Last, you know that 3 x + 6 = y, since they are vertical angles. Combining 2(x-11) and 2(x-10) and 2(3x+6) [remember, y = 3x + 6!!], you get that 10 x = 390, and x = 39. Plug that in for the value of y, which is 3x + 6, giving you 123 degrees.

i think it would be 43 movies that would have to be watched.

step-by-step explanation:

think about it. for the second plan, every month is 8 dollars. 8 x 12= 96. so thats the number for the second plan. now for the first plan, its annual meaning you have to pay 10 dollars every year. so now you have to get an equivalent amount of 86 since 96-10=86. 86 divided by 2 since every movie costs 2$ then you would have to watch 43 movies a year to get the same as the second plan. i really hoped this . have a wonderful day as well!