(02.06)in the figure below, lines m and n are parallel:

two parallel lines are shown crossed by a transversal. the angles are labeled with number 1-8. the angles on line m where the line is crossed by the transversal are 1, 2, 3, and 4 in clockwise order from top left. the angles on line n where the line is crossed by the transversal are 5, 6, 7, and 8 in clockwise order from top left.

in the diagram shown, ∠2 measures 77 degrees. what is the measure of ∠4?

5 degrees
77 degrees
103 degrees
180 degrees

"77 degrees"

Step-by-step explanation:

If you read the questions carefully, you will see that ∠2 and ∠4 are opposite angles to each other, or vertical angles.

We know that vertical angles are EQUAL to each other.

Hence,

∠4 = ∠2  [which is 77]

So, ∠4 = 77°

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

add 8+12 to get a simplified answer of 12r-20