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° = 156, the value of z° is 24.

A line segment is a portion of a line with a measurable length. The midpoint of a line segment is the point exactly halfway between the endpoints. The midpoint bisects (cuts in half) the line segment.

Perimeter is equal to the sum of the four sides:

p = a + b + c + d
p = 8 + 3 + 8 + 8
p = 27

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

c² - 17c + 72 = 0
(c - 8)(c - 9) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (c - 8) or (c - 9) must equal zero:

If (c - 8) = 0, c must equal 8
If (c - 9) = 0, c must equal 9

So the solution is that c = 8 or 9

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 4 as well and sum (Inside, Outside) to equal -5. For this problem, those two numbers are -4 and -1. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² - 5y + 4
y² + (-4 - 1)y + (-4 x -1)
(y - 4)(y - 1)