A rectangle is a parallelogram containing four right angles. Opposite sides (a = c, b = d) are equal and the perimeter is the sum of the lengths of all sides (a + b + c + d) or, comonly, 2 x length x width. The area of a rectangle is length x width. A square is a rectangle with four equal length sides. The perimeter of a square is 4 x length of one side (4s) and the area is the length of one side squared (s²).

The formula for area is πr²:

a = πr²
a = π(2²)
a = 4π

To multiply binomials, use the FOIL method. FOIL stands for First, Outside, Inside, Last and refers to the position of each term in the parentheses:

(y - 6)(y - 8)
(y x y) + (y x -8) + (-6 x y) + (-6 x -8)
y² - 8y - 6y + 48
y² - 14y + 48

The first step to solve a quadratic expression that's not set to zero is to solve the equation so that it is set to zero:

y² - 4y - 51 = -4y - 2
y² - 4y - 51 + 2 = -4y
y² - 4y + 4y - 49 = 0
y² - 49 = 0

Next, factor the quadratic equation:

y² - 49 = 0
(y - 7)(y + 7) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (y - 7) or (y + 7) must equal zero:

If (y - 7) = 0, y must equal 7
If (y + 7) = 0, y must equal -7

So the solution is that y = 7 or -7

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 x° = 152, the value of z° is 28.