An exterior angle of a triangle is equal to the sum of the two interior angles that are opposite:

d° = b° + c°

To find angle c, remember that the sum of the interior angles of a triangle is 180°:

180° = a° + b° + c°
c° = 180° - a° - b°
c° = 180° - 67° - 63° = 50°

So, d° = 63° + 50° = 113°

A shortcut to get this answer is to remember that angles around a line add up to 180°:

a° + d° = 180°
d° = 180° - a°
d° = 180° - 67° = 113°

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.

5c - 9 = \( \frac{c}{7} \)
7 x (5c - 9) = c
(7 x 5c) + (7 x -9) = c
35c - 63 = c
35c - 63 - c = 0
35c - c = 63
34c = 63
c = \( \frac{63}{34} \)
c = 1\(\frac{29}{34}\)

Parallel lines are lines that share the same slope (steepness) and therefore never intersect. A transversal occurs when a set of parallel lines are crossed by another line. All of the angles formed by a transversal are called interior angles and angles in the same position on different parallel lines equal each other (a° = w°, b° = x°, c° = z°, d° = y°) and are called corresponding angles. Alternate interior angles are equal (a° = z°, b° = y°, c° = w°, d° = x°) and 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°).

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.

-3c - 1 < \( \frac{c}{7} \)
7 x (-3c - 1) < c
(7 x -3c) + (7 x -1) < c
-21c - 7 < c
-21c - 7 - c < 0
-21c - c < 7
-22c < 7
c < \( \frac{7}{-22} \)
c < -\(\frac{7}{22}\)

A cylinder is a solid figure with straight parallel sides and a circular or oval cross section with a radius (r) and a height (h). The volume of a cylinder is π r²h and the surface area is 2(π r²) + 2π rh.