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° = 18, the value of d° is 162.

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

p = x + y + z
p = 10cm + 11cm + 8cm = 29cm

The slope-intercept equation for a line is y = mx + b where m is the slope and b is the y-intercept of the line. From the graph, you can see that the y-intercept (the y-value from the point where the line crosses the y-axis) is 1. The slope of this line is the change in y divided by the change in x. The endpoints of this line segment are at (-2, -5) and (2, 7) so the slope becomes:

m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(7.0) - (-5.0)}{(2) - (-2)} \) = \( \frac{12}{4} \)
m = 3

Plugging these values into the slope-intercept equation:

y = 3x + 1

To combine like terms, add or subtract the coefficients (the numbers that come before the variables) of terms that have the same variable raised to the same exponent.

7a⁹ - 3a⁹ = 4a⁹

The area of a parallelogram is equal to its length x width:

a = l x w
a = a x b
a = 6 x 9
a = 54