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 b° = 146, the value of d° is 146.

The circumference of a circle is the distance around its perimeter and equals π (approx. 3.14159) x diameter: c = π d. The area of a circle is π x (radius)² : a = π r².

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.

(6a)(4ab) + (7a²)(8b)
(6 x 4)(a x a x b) + (7 x 8)(a² x b)
(24)(a¹⁺¹ x b) + (56)(a²b)
24a²b + 56a²b
80a²b

The area of a triangle is equal to ½ base x height:

a = ½bh
a = ½ x 7 x 1 = \( \frac{7}{2} \) = 3\(\frac{1}{2}\)

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 3. 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, 1) and (2, 5) so the slope becomes:

Plugging these values into the slope-intercept equation:

y = x + 3