If you can with any questions on here ! with an explanation pls

6. The value of a = 18

7. The value of c = 72

8. a = 15 , b = 30 , c = 10

9. The sum = 900°

10. The measure = 164.3°

Step-by-step explanation:

In number 6.

∵ The figure is regular decagon (all sides are equal

∴ The measure of each vertex angle = [(10 - 2) × 180] ÷ 10 = 144°

∵ The triangle which contains a is isosceles Δ

∴ a = (180 - 144) ÷ 2 = 18°

In number 7.

∵ The figure which contains a and b is regular pentagon

∴ The measure of each vertex angle = [(5 - 2) × 180] ÷ 5 = 108

∵ c is an exterior angle to the regular polygon

∴ c = 180 - 108 = 72°

In number 8.

∵ The two lines are parallel and intersected by a transversal

∴ b = 3c ⇒ corresponding angles

∵ 3c + 5b = 180 ⇒ straight angle

∴ b + 5b = 180 ⇒ 6b = 180

∴ b = 180 ÷ 6 = 30

∵ b = 3c ⇒ ∴ 3c = 30

∴ c = 30 ÷ 3 = 10

∵ b = 2a ⇒ vertically opposite angles

∴ 2a = 30 ⇒ a = 30 ÷ 2 = 15

9. The sum of the interior angles of any polygon = (n - 2) × 180

    where n is the number of sides

The sum = (7 - 2) × 180 = 900°

10. The m of each interior angle of a regular polygon = [(n - 2) × 180] ÷ n

∴ The measure = [(23 - 2) × 180] ÷ 23 = 164.3°

when rotating a figure 180 degrees, imagine that you are able to take the figure and turn it clockwise or counterclockwise around a center point. to rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y). start by using a coordinate grid with coordinates for each vertex of the figure. the center point of the coordinate grid is located at (0, 0), which is what you will rotate the figure around. write down the original coordinates of the shape you are going to rotate. then, apply the rule. for example, coordinate (1, 2) becomes (-1, -2). another example would be, coordinate (-4, -2) becoming (4, 2). after you change each original coordinate to the rotated coordinate, you will draw your new figure.

step-by-step explanation:

493 would be the correct answer

step-by-step explanation: