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 b° = 153, the value of a° is 27.

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)(2ab) + (7a²)(5b)
(8 x 2)(a x a x b) + (7 x 5)(a² x b)
(16)(a¹⁺¹ x b) + (35)(a²b)
16a²b + 35a²b
51a²b

A monomial contains one term, a binomial contains two terms, and a polynomial contains more than two terms.

The formula for area is πr². Radius is circle \( \frac{diameter}{2} \):

r = \( \frac{d}{2} \)
r = \( \frac{10}{2} \)
r = 5
a = πr²
a = π(5²)
a = 25π

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 + 2)(y + 1)
(y x y) + (y x 1) + (2 x y) + (2 x 1)
y² + y + 2y + 2
y² + 3y + 2