Angles around a line add up to 180°. Angles around a point add up to 360°. When two lines intersect, adjacent angles are supplementary (they add up to 180°) and angles across from either other are vertical (they're equal).

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° = 151, the value of z° is 29.

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.

-8z + 4 > 2 + 3z
-8z > 2 + 3z - 4
-8z - 3z > 2 - 4
-11z > -2
z > \( \frac{-2}{-11} \)
z > \(\frac{2}{11}\)

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

a = ½bh
a = ½ x 9 x 3 = \( \frac{27}{2} \) = 13\(\frac{1}{2}\)

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 equal sign and the answer on the other.

6z - 7 = 8 - z
6z = 8 - z + 7
6z + z = 8 + 7
7z = 15
z = \( \frac{15}{7} \)
z = 2\(\frac{1}{7}\)