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 d° = 169, the value of c° is 11.

To multiply monomials, multiply the coefficients (the numbers that come before the variables) of each term, add the exponents of like variables, and multiply the different variables together.

(9a)(4ab) - (5a²)(8b)
(9 x 4)(a x a x b) - (5 x 8)(a² x b)
(36)(a¹⁺¹ x b) - (40)(a²b)
36a²b - 40a²b
-4a²b

The first step to solve a quadratic equation that's set to zero is to factor the quadratic equation:

c² + 6c + 5 = 0
(c + 1)(c + 5) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (c + 1) or (c + 5) must equal zero:

If (c + 1) = 0, c must equal -1
If (c + 5) = 0, c must equal -5

So the solution is that c = -1 or -5

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:

x² - 8x - 30 = -4x + 2
x² - 8x - 30 - 2 = -4x
x² - 8x + 4x - 32 = 0
x² - 4x - 32 = 0

Next, factor the quadratic equation:

x² - 4x - 32 = 0
(x + 4)(x - 8) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (x + 4) or (x - 8) must equal zero:

If (x + 4) = 0, x must equal -4
If (x - 8) = 0, x must equal 8

So the solution is that x = -4 or 8

To multiply monomials, multiply the coefficients (the numbers that come before the variables) of each term, add the exponents of like variables, and multiply the different variables together.

8a x 2b = (8 x 2) (a x b) = 16ab