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 x° = 148, the value of z° is 32.

To solve this equation, isolate the variable for which you are solving (a) on one side of the equation and put everything else on the other side.

-3a - 9y = -7a - 3y + 1
-3a = -7a - 3y + 1 + 9y
-3a + 7a = -3y + 1 + 9y
4a = 6y + 1
a = \( \frac{6y + 1}{4} \)
a = \( \frac{6y}{4} \) + \( \frac{1}{4} \)
a = 1\(\frac{1}{2}\)y + \(\frac{1}{4}\)

A trapezoid is a quadrilateral with one set of parallel sides.

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.

The surface area of a cylinder is 2πr² + 2πrh:

sa = 2πr² + 2πrh
sa = 2π(8²) + 2π(8 x 6)
sa = 2π(64) + 2π(48)
sa = (2 x 64)π + (2 x 48)π
sa = 128π + 96π
sa = 224π