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° - 23° - 69° = 88°

So, d° = 69° + 88° = 157°

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° - 23° = 157°

A quadrilateral is a shape with four sides. The perimeter of a quadrilateral is the sum of the lengths of its four sides.

To multiply monomials, multiply the coefficients (the numbers that come before the variables) of each term, add the exponents of like variables, and multiply the different variables together.

5a x 2b = (5 x 2) (a x b) = 10ab

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 equation that's set to zero is to factor the quadratic equation:

z² - 4z - 21 = 0
(z + 3)(z - 7) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (z + 3) or (z - 7) must equal zero:

If (z + 3) = 0, z must equal -3
If (z - 7) = 0, z must equal 7

So the solution is that z = -3 or 7