| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.88 |
| Score | 0% | 58% |
This diagram represents two parallel lines with a transversal. If c° = 12, what is the value of d°?
| 10 | |
| 168 | |
| 32 | |
| 37 |
For parallel lines with a transversal, the following relationships apply:
Applying these relationships starting with c° = 12, the value of d° is 168.
If angle a = 39° and angle b = 59° what is the length of angle d?
| 158° | |
| 157° | |
| 141° | |
| 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° - 39° - 59° = 82°
So, d° = 59° + 82° = 141°
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° - 39° = 141°
Which of the following is not true about both rectangles and squares?
the lengths of all sides are equal |
|
all interior angles are right angles |
|
the perimeter is the sum of the lengths of all four sides |
|
the area is length x width |
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).
Which of the following statements about parallel lines with a transversal is not correct?
angles in the same position on different parallel lines are called corresponding angles |
|
all acute angles equal each other |
|
same-side interior angles are complementary and equal each other |
|
all of the angles formed by a transversal are called interior angles |
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°).
Which of the following statements about a triangle is not true?
sum of interior angles = 180° |
|
perimeter = sum of side lengths |
|
area = ½bh |
|
exterior angle = sum of two adjacent interior angles |
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.