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°).

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

p = x + y + z
p = 15cm + 10cm + 7cm = 32cm

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:

z² - 11z + 16 = -2z - 4
z² - 11z + 16 + 4 = -2z
z² - 11z + 2z + 20 = 0
z² - 9z + 20 = 0

Next, factor the quadratic equation:

z² - 9z + 20 = 0
(z - 4)(z - 5) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (z - 4) or (z - 5) must equal zero:

If (z - 4) = 0, z must equal 4
If (z - 5) = 0, z must equal 5

So the solution is that z = 4 or 5

An acute angle measures less than 90°, a right angle measures 90°, and an obtuse angle measures more than 90°.