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.

The sum of the interior angles of a triangle is 180°:
180° = a° + b° + c°
c° = 180° - a° - b°
c° = 180° - 34° - 68° = 78°

To multiply binomials, use the FOIL method. FOIL stands for First, Outside, Inside, Last and refers to the position of each term in the parentheses.

The first step to solve a quadratic equation that's set to zero is to factor the quadratic equation:

y² + 8y + 12 = 0
(y + 2)(y + 6) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (y + 2) or (y + 6) must equal zero:

If (y + 2) = 0, y must equal -2
If (y + 6) = 0, y must equal -6

So the solution is that y = -2 or -6

An exterior angle of a triangle is equal to the sum of the two interior angles that are opposite:

d° = b° + c°

To find angle c, remember that the sum of the interior angles of a triangle is 180°:

180° = a° + b° + c°
c° = 180° - a° - b°
c° = 180° - 43° - 38° = 99°

So, d° = 38° + 99° = 137°

A shortcut to get this answer is to remember that angles around a line add up to 180°:

a° + d° = 180°
d° = 180° - a°
d° = 180° - 43° = 137°