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° = 162, the value of c° is 18.

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 - 47 = -2y + 1
y² - 4y - 47 - 1 = -2y
y² - 4y + 2y - 48 = 0
y² - 2y - 48 = 0

Next, factor the quadratic equation:

y² - 2y - 48 = 0
(y + 6)(y - 8) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (y + 6) or (y - 8) must equal zero:

If (y + 6) = 0, y must equal -6
If (y - 8) = 0, y must equal 8

So the solution is that y = -6 or 8

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 equal sign and the answer on the other.

2b + 2 = \( \frac{b}{8} \)
8 x (2b + 2) = b
(8 x 2b) + (8 x 2) = b
16b + 16 = b
16b + 16 - b = 0
16b - b = -16
15b = -16
b = \( \frac{-16}{15} \)
b = -1\(\frac{1}{15}\)

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 equal sign and the answer on the other.

-5a - 9 = -4 - 7a
-5a = -4 - 7a + 9
-5a + 7a = -4 + 9
2a = 5
a = \( \frac{5}{2} \)
a = 2\(\frac{1}{2}\)

To combine like terms, add or subtract the coefficients (the numbers that come before the variables) of terms that have the same variable raised to the same exponent.

8a⁸ + 2a⁸ = 10a⁸