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.

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° - 32° - 42° = 106°

So, d° = 42° + 106° = 148°

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° - 32° = 148°

You need to find the value of b so solve the first equation in terms of x:

-3b + x = -5
x = -5 + 3b

then substitute the result (-5 - -3b) into the second equation:

-2b + 9(-5 + 3b) = 3
-2b + (9 x -5) + (9 x 3b) = 3
-2b - 45 + 27b = 3
-2b + 27b = 3 + 45
25b = 48
b = \( \frac{48}{25} \)
b = 1\(\frac{23}{25}\)

A rectangle is a parallelogram containing four right angles. Opposite sides (a = c, b = d) are equal and the perimeter is the sum of the lengths of all sides (a + b + c + d) or, comonly, 2 x length x width. The area of a rectangle is length x width. A square is a rectangle with four equal length sides. The perimeter of a square is 4 x length of one side (4s) and the area is the length of one side squared (s²).

The volume of a cylinder is πr²h:

v = πr²h
v = π(5² x 1)
v = 25π