For parallel lines with a transversal, the following relationships apply:

• angles in the same position on different parallel lines equal each other (a° = w°, b° = x°, c° = z°, d° = y°)
• alternate interior angles are equal (a° = z°, b° = y°, c° = w°, d° = x°)
• all acute angles (a° = c° = w° = z°) and all obtuse angles (b° = d° = x° = y°) equal each other
• same-side interior angles are supplementary and add up to 180° (e.g. a° + d° = 180°, d° + c° = 180°)

Applying these relationships starting with w° = 23, the value of c° is 23.

To solve this equation, isolate the variable for which you are solving (c) on one side of the equation and put everything else on the other side.

-9c + 9y = 7c - 5y - 9
-9c = 7c - 5y - 9 - 9y
-9c - 7c = -5y - 9 - 9y
-16c = -14y - 9
c = \( \frac{-14y - 9}{-16} \)
c = \( \frac{-14y}{-16} \) + \( \frac{-9}{-16} \)
c = \(\frac{7}{8}\)y + \(\frac{9}{16}\)

To solve this equation, repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the > sign and the answer on the other.

b - 2 > \( \frac{b}{9} \)
9 x (b - 2) > b
(9 x b) + (9 x -2) > b
9b - 18 > b
9b - 18 - b > 0
9b - b > 18
8b > 18
b > \( \frac{18}{8} \)
b > 2\(\frac{1}{4}\)

A circle is a figure in which each point around its perimeter is an equal distance from the center. The radius of a circle is the distance between the center and any point along its perimeter. A chord is a line segment that connects any two points along its perimeter. The diameter of a circle is the length of a chord that passes through the center of the circle and equals twice the circle's radius (2r).

The surface area of a cube is (2 x length x width) + (2 x width x height) + (2 x length x height):

sa = 2lw + 2wh + 2lh
sa = (2 x 6 x 7) + (2 x 7 x 3) + (2 x 6 x 3)
sa = (84) + (42) + (36)
sa = 162