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.

A circle is a figure in which each point around its perimeter is an equal distance from the center. The radius of a circle is the distance between the center and any point along its perimeter. A chord is a line segment that connects any two points along its perimeter. The diameter of a circle is the length of a chord that passes through the center of the circle and equals twice the circle's radius (2r).

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° - 58° - 41° = 81°

So, d° = 41° + 81° = 122°

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° - 58° = 122°

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 < sign and the answer on the other.

6y + 3 < -8 - 6y
6y < -8 - 6y - 3
6y + 6y < -8 - 3
12y < -11
y < \( \frac{-11}{12} \)
y < -\(\frac{11}{12}\)

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

c² - 11c + 24 = 0
(c - 3)(c - 8) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (c - 3) or (c - 8) must equal zero:

If (c - 3) = 0, c must equal 3
If (c - 8) = 0, c must equal 8

So the solution is that c = 3 or 8