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° - 65° - 55° = 60°

So, d° = 55° + 60° = 115°

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° - 65° = 115°

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.

3z + 1 < \( \frac{z}{-5} \)
-5 x (3z + 1) < z
(-5 x 3z) + (-5 x 1) < z
-15z - 5 < z
-15z - 5 - z < 0
-15z - z < 5
-16z < 5
z < \( \frac{5}{-16} \)
z < -\(\frac{5}{16}\)

A rectangle is a parallelogram containing four right angles. Opposite sides (a = c, b = d) are equal and the perimeter is the sum of the lengths of all sides (a + b + c + d) or, comonly, 2 x length x width. The area of a rectangle is length x width. A square is a rectangle with four equal length sides. The perimeter of a square is 4 x length of one side (4s) and the area is the length of one side squared (s²).

The perimeter of a triangle is the sum of the lengths of its sides:

p = x + y + z
p = 7cm + 12cm + 7cm = 26cm

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:

x² - 11x + 28 = -x + 3
x² - 11x + 28 - 3 = -x
x² - 11x + x + 25 = 0
x² - 10x + 25 = 0

Next, factor the quadratic equation:

x² - 10x + 25 = 0
(x - 5)(x - 5) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, (x - 5) must equal zero:

If (x - 5) = 0, x must equal 5

So the solution is that x = 5