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 d° is 153.

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

To multiply monomials, multiply the coefficients (the numbers that come before the variables) of each term, add the exponents of like variables, and multiply the different variables together.

9a x 6b = (9 x 6) (a x b) = 54ab

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 < sign and the answer on the other.

-5y + 5 < \( \frac{y}{-1} \)
-1 x (-5y + 5) < y
(-1 x -5y) + (-1 x 5) < y
5y - 5 < y
5y - 5 - y < 0
5y - y < 5
4y < 5
y < \( \frac{5}{4} \)
y < 1\(\frac{1}{4}\)

A line on the coordinate grid can be defined by a slope-intercept equation: y = mx + b. For a given value of x, the value of y can be determined given the slope (m) and y-intercept (b) of the line. The slope of a line is change in y over change in x, \({\Delta y \over \Delta x}\), and the y-intercept is the y-coordinate where the line crosses the vertical y-axis.