The entire length of this line is represented by AD which is AB + BD:

AD = AB + BD

The sum of the interior angles of a triangle is 180°:
180° = a° + b° + c°
c° = 180° - a° - b°
c° = 180° - 40° - 41° = 99°

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.

4x + 9 = -4 + 3x
4x = -4 + 3x - 9
4x - 3x = -4 - 9
x = -13

To factor a quadratic expression, apply the FOIL method (First, Outside, Inside, Last) in reverse. First, find the two Last terms that will multiply to produce 8 as well and sum (Inside, Outside) to equal 9. For this problem, those two numbers are 1 and 8. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² + 9y + 8
y² + (1 + 8)y + (1 x 8)
(y + 1)(y + 8)

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 z° = 37, the value of c° is 37.