| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.31 |
| Score | 0% | 66% |
If angle a = 46° and angle b = 30° what is the length of angle d?
| 134° | |
| 155° | |
| 160° | |
| 119° |
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° - 46° - 30° = 104°
So, d° = 30° + 104° = 134°
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° - 46° = 134°
Order the following types of angle from least number of degrees to most number of degrees.
right, obtuse, acute |
|
acute, right, obtuse |
|
right, acute, obtuse |
|
acute, obtuse, right |
An acute angle measures less than 90°, a right angle measures 90°, and an obtuse angle measures more than 90°.
The dimensions of this cube are height (h) = 5, length (l) = 4, and width (w) = 3. What is the volume?
| 27 | |
| 60 | |
| 168 | |
| 72 |
The volume of a cube is height x length x width:
v = h x l x w
v = 5 x 4 x 3
v = 60
Solve for c:
c2 - 9c + 5 = c - 4
| 5 or 5 | |
| 1 or 9 | |
| 9 or 8 | |
| -6 or -9 |
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:
c2 - 9c + 5 = c - 4
c2 - 9c + 5 + 4 = c
c2 - 9c - c + 9 = 0
c2 - 10c + 9 = 0
Next, factor the quadratic equation:
c2 - 10c + 9 = 0
(c - 1)(c - 9) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (c - 1) or (c - 9) must equal zero:
If (c - 1) = 0, c must equal 1
If (c - 9) = 0, c must equal 9
So the solution is that c = 1 or 9
If angle a = 36° and angle b = 51° what is the length of angle c?
| 105° | |
| 93° | |
| 82° | |
| 99° |
The sum of the interior angles of a triangle is 180°:
180° = a° + b° + c°
c° = 180° - a° - b°
c° = 180° - 36° - 51° = 93°