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).

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 z° = 27, the value of b° is 153.

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

p = x + y + z
p = 15cm + 14cm + 6cm = 35cm

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.

6a + 1 = \( \frac{a}{3} \)
3 x (6a + 1) = a
(3 x 6a) + (3 x 1) = a
18a + 3 = a
18a + 3 - a = 0
18a - a = -3
17a = -3
a = \( \frac{-3}{17} \)
a = -\(\frac{3}{17}\)

The entire length of this line is represented by AD which is AB + BD:

AD = AB + BD