| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.24 |
| Score | 0% | 65% |
If angle a = 21° and angle b = 67° what is the length of angle c?
| 115° | |
| 92° | |
| 65° | |
| 110° |
The sum of the interior angles of a triangle is 180°:
180° = a° + b° + c°
c° = 180° - a° - b°
c° = 180° - 21° - 67° = 92°
A trapezoid is a quadrilateral with one set of __________ sides.
equal angle |
|
parallel |
|
right angle |
|
equal length |
A trapezoid is a quadrilateral with one set of parallel sides.
What is 4a - 7a?
| 28a | |
| -3a | |
| a2 | |
| -3a2 |
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.
4a - 7a = -3a
If angle a = 54° and angle b = 38° what is the length of angle d?
| 124° | |
| 148° | |
| 155° | |
| 126° |
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° - 54° - 38° = 88°
So, d° = 38° + 88° = 126°
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° - 54° = 126°
Solve for c:
c2 - 37 = 2c - 2
| 3 or -9 | |
| 1 or -4 | |
| -7 or -9 | |
| -5 or 7 |
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 - 37 = 2c - 2
c2 - 37 + 2 = 2c
c2 - 2c - 35 = 0
c2 - 2c - 35 = 0
Next, factor the quadratic equation:
c2 - 2c - 35 = 0
(c + 5)(c - 7) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (c + 5) or (c - 7) must equal zero:
If (c + 5) = 0, c must equal -5
If (c - 7) = 0, c must equal 7
So the solution is that c = -5 or 7