Parallel lines are lines that share the same slope (steepness) and therefore never intersect. A transversal occurs when a set of parallel lines are crossed by another line. All of the angles formed by a transversal are called interior angles and angles in the same position on different parallel lines equal each other (a° = w°, b° = x°, c° = z°, d° = y°) and are called corresponding angles. Alternate interior angles are equal (a° = z°, b° = y°, c° = w°, d° = x°) and 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°).

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.

7c + 8z = -c - z + 9
7c = -c - z + 9 - 8z
7c + c = -z + 9 - 8z
8c = -9z + 9
c = \( \frac{-9z + 9}{8} \)
c = \( \frac{-9z}{8} \) + \( \frac{9}{8} \)
c = -1\(\frac{1}{8}\)z + 1\(\frac{1}{8}\)

The Pythagorean theorem defines the relationship between the side lengths of a right triangle. The length of the hypotenuse squared (c²) is equal to the sum of the two perpendicular sides squared (a² + b²): c² = a² + b² or, solved for c, \(c = \sqrt{a + b}\)

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

a = l x w
a = a x b
a = 4 x 7
a = 28

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.)

4a(a - x)
4(7)(7 + 5)
4(7)(12)
(28)(12)
336