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.

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° = 32, the value of x° is 148.

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

x² + 13x + 42 = 0
(x + 6)(x + 7) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (x + 6) or (x + 7) must equal zero:

If (x + 6) = 0, x must equal -6
If (x + 7) = 0, x must equal -7

So the solution is that x = -6 or -7

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

c² = a² + b²
c² = 8² + 1²
c² = 64 + 1
c² = 65
c = \( \sqrt{65} \)

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:

x² + 4x - 51 = 2x - 3
x² + 4x - 51 + 3 = 2x
x² + 4x - 2x - 48 = 0
x² + 2x - 48 = 0

Next, factor the quadratic equation:

x² + 2x - 48 = 0
(x - 6)(x + 8) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (x - 6) or (x + 8) must equal zero:

If (x - 6) = 0, x must equal 6
If (x + 8) = 0, x must equal -8

So the solution is that x = 6 or -8