A triangle is a three-sided polygon. It has three interior angles that add up to 180° (a + b + c = 180°). An exterior angle of a triangle is equal to the sum of the two interior angles that are opposite (d = b + c). The perimeter of a triangle is equal to the sum of the lengths of its three sides, the height of a triangle is equal to the length from the base to the opposite vertex (angle) and the area equals one-half triangle base x height: a = ½ base x height.

To factor a quadratic expression, apply the FOIL (First, Outside, Inside, Last) method in reverse.

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 y° = 159, the value of a° is 21.

To combine like terms, add or subtract the coefficients (the numbers that come before the variables) of terms that have the same variable raised to the same exponent.

8a⁵ - 8a⁵ = 0a⁵

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.

-9b + y = 7b + 2y + 8
-9b = 7b + 2y + 8 - y
-9b - 7b = 2y + 8 - y
-16b = y + 8
b = \( \frac{y + 8}{-16} \)
b = \( \frac{y}{-16} \) + \( \frac{8}{-16} \)
b = -\(\frac{1}{16}\)y - \(\frac{1}{2}\)