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 y° = 164, the value of z° is 16.

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.

-6b + 3 = 8 + 9b
-6b = 8 + 9b - 3
-6b - 9b = 8 - 3
-15b = 5
b = \( \frac{5}{-15} \)
b = -\(\frac{1}{3}\)

A quadrilateral is a shape with four sides. The perimeter of a quadrilateral is the sum of the lengths of its four sides.

A parallelogram is a quadrilateral with two sets of parallel sides. Opposite sides (a = c, b = d) and angles (red = red, blue = blue) are equal. The area of a parallelogram is base x height and the perimeter is the sum of the lengths of all sides (a + b + c + d).

To factor a quadratic expression, apply the FOIL method (First, Outside, Inside, Last) in reverse. First, find the two Last terms that will multiply to produce 24 as well and sum (Inside, Outside) to equal 11. For this problem, those two numbers are 3 and 8. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² + 11y + 24
y² + (3 + 8)y + (3 x 8)
(y + 3)(y + 8)