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).

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° - 59° - 35° = 86°

So, d° = 35° + 86° = 121°

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° - 59° = 121°

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.

5a - 3a = 2a

The first step to solve a quadratic expression that's not set to zero is to solve the equation so that it is set to zero:

a² - 4a - 4 = -3a - 2
a² - 4a - 4 + 2 = -3a
a² - 4a + 3a - 2 = 0
a² - a - 2 = 0

Next, factor the quadratic equation:

a² - a - 2 = 0
(a + 1)(a - 2) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (a + 1) or (a - 2) must equal zero:

If (a + 1) = 0, a must equal -1
If (a - 2) = 0, a must equal 2

So the solution is that a = -1 or 2

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.