Parallel lines are lines that share the same slope (steepness) and therefore never intersect. A transversal occurs when a set of parallel lines are crossed by another line. All of the angles formed by a transversal are called interior angles and angles in the same position on different parallel lines equal each other (a° = w°, b° = x°, c° = z°, d° = y°) and are called corresponding angles. Alternate interior angles are equal (a° = z°, b° = y°, c° = w°, d° = x°) and 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°).

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

p = x + y + z
p = 11cm + 11cm + 14cm = 36cm

To multiply binomials, use the FOIL method. FOIL stands for First, Outside, Inside, Last and refers to the position of each term in the parentheses:

(y + 7)(y + 8)
(y x y) + (y x 8) + (7 x y) + (7 x 8)
y² + 8y + 7y + 56
y² + 15y + 56

Perimeter is equal to the sum of the four sides:

p = a + b + c + d
p = 9 + 9 + 8 + 6
p = 32

You need to find the value of c so solve the first equation in terms of x:

9c + x = -1
x = -1 - 9c

then substitute the result (-1 - 9c) into the second equation:

-8c - 8(-1 - 9c) = 1
-8c + (-8 x -1) + (-8 x -9c) = 1
-8c + 8 + 72c = 1
-8c + 72c = 1 - 8
64c = -7
c = \( \frac{-7}{64} \)
c = -\(\frac{7}{64}\)