An equation is two expressions separated by an equal sign. The key to solving equations is to repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the equal sign and the answer on the other.

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).

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

7c + x = 8
x = 8 - 7c

then substitute the result (8 - 7c) into the second equation:

-9c + 8(8 - 7c) = 1
-9c + (8 x 8) + (8 x -7c) = 1
-9c + 64 - 56c = 1
-9c - 56c = 1 - 64
-65c = -63
c = \( \frac{-63}{-65} \)
c = \(\frac{63}{65}\)

For parallel lines with a transversal, the following relationships apply:

• angles in the same position on different parallel lines equal each other (a° = w°, b° = x°, c° = z°, d° = y°)
• alternate interior angles are equal (a° = z°, b° = y°, c° = w°, d° = x°)
• 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°)

Applying these relationships starting with w° = 23, the value of a° is 23.

The area of a trapezoid is one-half the sum of the lengths of the parallel sides multiplied by the height:

a = ½(b + d)(h)
a = ½(4 + 3)(2)
a = ½(7)(2)
a = ½(14) = \( \frac{14}{2} \)
a = 7