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 z° = 35, the value of w° is 35.

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

c + 8z = 9c + 3z - 4
c = 9c + 3z - 4 - 8z
c - 9c = 3z - 4 - 8z
-8c = -5z - 4
c = \( \frac{-5z - 4}{-8} \)
c = \( \frac{-5z}{-8} \) + \( \frac{-4}{-8} \)
c = \(\frac{5}{8}\)z + \(\frac{1}{2}\)

The perimeter of a triangle is the sum of the lengths of its sides:

p = x + y + z
p = 9cm + 13cm + 6cm = 28cm

To solve this equation, replace the variables with the values given and then solve the now variable-free equation. (Remember order of operations, PEMDAS, Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.)

7c(c - y)
7(-4)(-4 + 1)
7(-4)(-3)
(-28)(-3)
84

The area of a rectangle is equal to its length x width:

a = l x w
a = a x b
a = 7 x 1
a = 7