Lines m and n are parallel, solve for the following values of x. Tell which theorem you used(name the angle pair)

x = 90  (Alternate exterior angles)

Step-by-step explanation:

Given that,

Lines m and n are parallel.

We need to find the value of x.

Here, (180-x) will be equal to x as the alternate exterior angles are equal. So,

(180-x) = x

180 = 2x

x = 90

So, the value of x is equal to 90°.

9 sandwiches per hour

step-by-step explanation:

when we have a rate, we want a 1 in the denominator

27/3 = 9

27 sandwiches/ 3 hours = 9 sandwiches/hour

d 25 pi/6

step-by-step explanation:

the diameter is 10 inches

the radius is 1/2 of the diameter or 5 inches

the area of the circle is

a = pi r^2

  = pi 5^2

  = 25 pi

the slice is 60 degrees of the entire circle.

60 degrees out of 360   60/360 = 1/6

the area of the slice is 1/6 of the circle

a slice = 1/6 a circle

a slice = 1/6 * 25 pi