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 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.

-8b + 9 = \( \frac{b}{3} \)
3 x (-8b + 9) = b
(3 x -8b) + (3 x 9) = b
-24b + 27 = b
-24b + 27 - b = 0
-24b - b = -27
-25b = -27
b = \( \frac{-27}{-25} \)
b = 1\(\frac{2}{25}\)

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.

2y - 8 = 1 + 7y
2y = 1 + 7y + 8
2y - 7y = 1 + 8
-5y = 9
y = \( \frac{9}{-5} \)
y = -1\(\frac{4}{5}\)

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° = 169, the value of a° is 11.

A trapezoid is a quadrilateral with one set of parallel sides.