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

c² - 4c - 5 = 0
(c + 1)(c - 5) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (c + 1) or (c - 5) must equal zero:

If (c + 1) = 0, c must equal -1
If (c - 5) = 0, c must equal 5

So the solution is that c = -1 or 5

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 c° = 24, the value of b° is 156.

Perimeter is equal to the sum of the four sides:

p = a + b + c + d
p = 2 + 8 + 7 + 9
p = 26