The first step to solve a quadratic equation that's set to zero is to factor the quadratic equation:

x² - 15x + 54 = 0
(x - 6)(x - 9) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (x - 6) or (x - 9) must equal zero:

If (x - 6) = 0, x must equal 6
If (x - 9) = 0, x must equal 9

So the solution is that x = 6 or 9

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 b° is 157.

A triangle is a three-sided polygon. It has three interior angles that add up to 180° (a + b + c = 180°). An exterior angle of a triangle is equal to the sum of the two interior angles that are opposite (d = b + c). The perimeter of a triangle is equal to the sum of the lengths of its three sides, the height of a triangle is equal to the length from the base to the opposite vertex (angle) and the area equals one-half triangle base x height: a = ½ base x height.

Perimeter is equal to the sum of the four sides:

p = a + b + c + d
p = 6 + 8 + 5 + 2
p = 21

According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:

c² = a² + b²
c² = 1² + 7²
c² = 1 + 49
c² = 50
c = \( \sqrt{50} \)