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° = 160, the value of z° is 20.

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

r = \( \frac{d}{2} \)
r = \( \frac{8}{2} \)
r = 4
a = πr²
a = π(4²)
a = 16π

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.

(7a)(4ab) + (5a²)(9b)
(7 x 4)(a x a x b) + (5 x 9)(a² x b)
(28)(a¹⁺¹ x b) + (45)(a²b)
28a²b + 45a²b
73a²b

An exterior angle of a triangle is equal to the sum of the two interior angles that are opposite:

d° = b° + c°

To find angle c, remember that the sum of the interior angles of a triangle is 180°:

180° = a° + b° + c°
c° = 180° - a° - b°
c° = 180° - 28° - 29° = 123°

So, d° = 29° + 123° = 152°

A shortcut to get this answer is to remember that angles around a line add up to 180°:

a° + d° = 180°
d° = 180° - a°
d° = 180° - 28° = 152°

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

2a + 9x = 3a - 8x - 9
2a = 3a - 8x - 9 - 9x
2a - 3a = -8x - 9 - 9x
-a = -17x - 9
a = \( \frac{-17x - 9}{-1} \)
a = \( \frac{-17x}{-1} \) + \( \frac{-9}{-1} \)
a = 17x + 9