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° - 61° - 45° = 74°

So, d° = 45° + 74° = 119°

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° - 61° = 119°

The circumference of a circle is the distance around its perimeter and equals π (approx. 3.14159) x diameter: c = π d. The area of a circle is π x (radius)² : a = π r².

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).

The first step to solve a quadratic expression that's not set to zero is to solve the equation so that it is set to zero:

c² - 19c + 43 = -5c - 5
c² - 19c + 43 + 5 = -5c
c² - 19c + 5c + 48 = 0
c² - 14c + 48 = 0

Next, factor the quadratic equation:

c² - 14c + 48 = 0
(c - 6)(c - 8) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (c - 6) or (c - 8) must equal zero:

If (c - 6) = 0, c must equal 6
If (c - 8) = 0, c must equal 8

So the solution is that c = 6 or 8

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.

5b - 4z = -3b - 4z + 1
5b = -3b - 4z + 1 + 4z
5b + 3b = -4z + 1 + 4z
8b = + 1
b = \( \frac{ + 1}{8} \)
b = \( \frac{}{8} \) + \( \frac{1}{8} \)
b = z + \(\frac{1}{8}\)