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°).

You need to find the value of c so solve the first equation in terms of x:

-c + x = 1
x = 1 + c

then substitute the result (1 - -1c) into the second equation:

2c + 9(1 + c) = 7
2c + (9 x 1) + (9 x c) = 7
2c + 9 + 9c = 7
2c + 9c = 7 - 9
11c = -2
c = \( \frac{-2}{11} \)
c = -\(\frac{2}{11}\)

An equation is two expressions separated by an equal sign. The key to solving equations is to 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.

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

-7b - 8x = 3b + 6x - 8
-7b = 3b + 6x - 8 + 8x
-7b - 3b = 6x - 8 + 8x
-10b = 14x - 8
b = \( \frac{14x - 8}{-10} \)
b = \( \frac{14x}{-10} \) + \( \frac{-8}{-10} \)
b = -1\(\frac{2}{5}\)x + \(\frac{4}{5}\)

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).