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.

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 d° = 159, the value of c° is 21.

A right angle measures 90 degrees and is the intersection of two perpendicular lines. In diagrams, a right angle is indicated by a small box completing a square with the perpendicular lines.

The area of a triangle is equal to ½ base x height:

a = ½bh
a = ½ x 2 x 3 = \( \frac{6}{2} \) = 3

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 equal sign and the answer on the other.

2a + 6 = \( \frac{a}{-4} \)
-4 x (2a + 6) = a
(-4 x 2a) + (-4 x 6) = a
-8a - 24 = a
-8a - 24 - a = 0
-8a - a = 24
-9a = 24
a = \( \frac{24}{-9} \)
a = -2\(\frac{2}{3}\)