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What is the name of the quadrilateral in the diagram?
A.
Trapezoid
B.
Rectangle
C.
Rhombus
D.
Parallelogram
Correct Answer D. Parallelogram
Explanation The quadrilateral in the diagram is a parallelogram because it has two pairs of parallel sides. A parallelogram is a four-sided polygon with opposite sides that are parallel and equal in length. It can also be identified by its opposite angles being equal. In the given diagram, the sides AB and CD are parallel, as well as the sides BC and AD. Therefore, the correct name for the quadrilateral in the diagram is parallelogram.
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2.
What is x in the parallelogram below?
A.
90
B.
6
C.
22
D.
12
Correct Answer B. 6
Explanation In a parallelogram, opposite angles are equal. Therefore, if one angle is 6, then the opposite angle must also be 6.
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3.
What is the measure of angel 1 in the parallelogram below?
A.
54Â°
B.
126Â°
C.
36Â°
D.
180Â°
Correct Answer B. 126Â°
Explanation In a parallelogram, opposite angles are congruent. Since the measure of angle 1 is not given directly, we can determine it by finding the measure of the opposite angle. The given answer of 126Â° is correct because it is the measure of the opposite angle to angle 1 in the parallelogram.
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4.
What is the measure of angle J in the parallelogram below?
A.
22
B.
64
C.
87
D.
93
Correct Answer D. 93
Explanation In a parallelogram, opposite angles are congruent. Since angle J is opposite to angle 87, they must have the same measure. Therefore, angle J is also 87 degrees.
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5.
A.
HI = 31
B.
HI = 6
C.
HI = 7.4
D.
GH = 3.6
E.
GH = 8.4
F.
GH = 7.4
G.
Angle I = 31
H.
Angle I = 6
I.
Angle I = 68
Correct Answer(s) B. HI = 6 D. GH = 3.6 G. Angle I = 31
6.
If angle C=65 an angle E = 5X, what is x?
A.
13Â°
B.
25Â°
C.
65Â°
D.
90Â°
Correct Answer A. 13Â°
Explanation Since angle C is given as 65Â° and angle E is represented as 5X, we can set up an equation: 5X = 65. Solving for X, we divide both sides by 5 to get X = 13. Therefore, the value of X is 13Â°.
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7.
In the rectangle ABCD below, AB = 4, BC = 8. Find the length of AD.
Correct Answer 8 AD=8
Explanation In a rectangle, opposite sides are equal in length. Therefore, if BC is 8 units long, then AD must also be 8 units long in order to maintain the rectangular shape.
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8.
Which of the following are true about rectangles?I. Their opposite sides are congruent.II. They have four right angles.III. Their diagonals are congruent.
A.
I only
B.
II only
C.
III only
D.
I and II only
E.
I, II and III
Correct Answer E. I, II and III
Explanation Rectangles are quadrilaterals with four right angles. Therefore, statement II is true. Additionally, rectangles have opposite sides that are congruent, as opposite sides are parallel and congruent. This makes statement I true. Lastly, the diagonals of a rectangle are congruent, as they bisect each other and form right angles. Hence, statement III is also true. Therefore, the correct answer is I, II, and III.
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9.
Given parallelogram ABCD, find the measure of angle A if angle B = 130 degrees.
Correct Answer 50 50 degrees A=50
Explanation The measure of angle A in parallelogram ABCD is 50 degrees. This can be determined by using the property of opposite angles in a parallelogram. Since angle B is given as 130 degrees, angle A, which is opposite to angle B, will also be 130 degrees. However, the sum of the measures of angles in a parallelogram is always 360 degrees. Therefore, angle A can be found by subtracting the measure of angle B from 360 degrees, which gives us 360 - 130 = 230 degrees. However, since angle A is opposite to angle B, it will have the same measure as angle B, which is 130 degrees. Therefore, the measure of angle A is 130 degrees.
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10.
In parallelogram ABCD, angle A = 2x + 20 degrees and angle B = 4x + 10 degrees.Find the measure of angle A.
Correct Answer 70 70 degrees A=70
Explanation The measure of angle A in parallelogram ABCD is 70 degrees. This is determined by setting the given equation equal to 70 and solving for x. By substituting x = 25 into the equation for angle A, we find that angle A = 2(25) + 20 = 70 degrees.
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11.
If angle C=65 an angle E = 13X, what is x?
A.
13Â°
B.
1.9Â°
C.
5Â°
D.
90Â°
Correct Answer C. 5Â°
Explanation Since angle E is equal to 13X, and angle C is equal to 65, we can set up the equation 13X = 65. By dividing both sides of the equation by 13, we find that X = 5. Therefore, the value of X is 5Â°.
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12.
If DE = 7, what is BD?
Correct Answer 14 BD=14
Explanation The given information states that DE is equal to 7. Therefore, if BD is equal to 14, it means that BD is twice the length of DE. This implies that BD is equal to 2 times 7, which equals 14. Hence, the answer is 14 and BD is indeed equal to 14.
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13.
In the rectangle below, AE = 4x + 3 and CE = 3x + 5. Find the length of AC.Remember to solve for x and then plug it back in to the expressions for AE and CE.
Correct Answer 22 AC=22
14.
In parallelogram ABCD, BE = 5x - 4 and DE = 3x + 8. Find the length of BD.
Correct Answer 52 BD=52
Explanation The length of BD in parallelogram ABCD is 52.
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15.
Quadrilateral ABCD is a rectangle.If angle ADB = 7k + 10 and angle CDB = 8k - 55, find angle CBD.
A.
16
B.
17
C.
74
D.
73
Correct Answer D. 73
Explanation In a rectangle, opposite angles are equal. Therefore, angle ADB is equal to angle CDB. We are given that angle ADB is 7k + 10 and angle CDB is 8k - 55. Since they are equal, we can set them equal to each other and solve for k. 7k + 10 = 8k - 55. Simplifying this equation, we get k = 65. Now that we know the value of k, we can substitute it back into either angle ADB or CDB to find the measure of angle CBD. Plugging k = 65 into angle ADB, we get angle CBD = 7(65) + 10 = 465 + 10 = 475. However, since angles in a quadrilateral sum up to 360 degrees, we subtract 360 from 475 to get the final answer of 115 degrees.
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16.
A.
EG = 8.4
B.
EG = 4.5
C.
EG = 4.1
D.
Angle G = 156
E.
Angle G = 66
F.
Angle G = 3.0
G.
EF = 9.1
H.
EF = 4.5
I.
EF = 3.0
Correct Answer(s) C. EG = 4.1 E. Angle G = 66 G. EF = 9.1
17.
In the parallelogram below, what is the measure of angle F?
A.
61
B.
139
C.
119
D.
34.75
Correct Answer A. 61
Explanation To find the measure of angle F, we need to solve the equation(4x - 20)° = 61°, as opposite angles in a parallelogram are equal.
Let’s solve this equation:
4x - 20 = 61
4x = 61 + 20
4x = 81
x = 81/4
x = 20.25
So, the value of x is 20.25. Now, let’s substitute x into the expression for angle F:
F = 4x - 20
F = 4(20.25) - 20
F = 81 - 20
F = 61°
Therefore, the measure of angle F is 61°.
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18.
Find the values of x and y in the diagram giving reasons for your answer.
Explanation The given answer states that the values of x and y in the diagram are x=115 and y=65. This is the correct answer because it matches the information provided in the question. The question asks us to find the values of x and y, and the answer states that x=115 and y=65. Therefore, the answer is correct.
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19.
In parallelogram ABCD, angle B = 3x + 20 degrees and angle D = 4x - 10 degrees. Find x.
Correct Answer 30 30 degrees x=30
Explanation The sum of the angles in a parallelogram is 360 degrees. Therefore, we can set up the equation: (3x + 20) + (4x - 10) = 360. Simplifying the equation gives us 7x + 10 = 360. Subtracting 10 from both sides gives us 7x = 350. Dividing both sides by 7 gives us x = 50. Therefore, the value of x is 50.
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20.
In parallelogram ABCD, angle A = 2x + 20 degrees and angle B = 4x + 10 degrees.Find the measure of angle B.
Correct Answer 110 110 degrees B=110
Explanation The measure of angle B in parallelogram ABCD is 110 degrees. This can be determined by setting the measure of angle A equal to the measure of angle B (since opposite angles in a parallelogram are congruent) and solving for x. By substituting x back into the equation for angle B, we can find that the measure of angle B is indeed 110 degrees.
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21.
In parallelogram ABCD, diagonal AC = 32 and AE = 4x. Find x.
Correct Answer 4 x=4
Explanation In a parallelogram, the diagonals bisect each other. Therefore, AC is equal to BD. Given that AC = 32, we can conclude that BD is also equal to 32. Since AE is a diagonal, it is equal to BD. So, AE = 32. It is also given that AE = 4x. By equating the two expressions for AE, we get 4x = 32. Dividing both sides by 4, we find that x = 8. Hence, the value of x is 8.
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22.
Quadrilateral ABCD is a rectangle.If AG = 2j + 21 and DG = - j + 39, find BD.
A.
33
B.
6
C.
66
D.
16.5
Correct Answer C. 66
Explanation Since ABCD is a rectangle, opposite sides are equal in length. Therefore, AG = DG. We can set up an equation using this information:
2j + 21 = -j + 39
Solving this equation, we find j = 6.
Now, we can substitute the value of j back into either AG or DG to find its length. Using AG:
AG = 2(6) + 21 = 33
Since opposite sides of a rectangle are equal, BD is also equal to 33.
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23.
What is the measure of angle J in the parallelogram below?
A.
22
B.
83
C.
97
D.
93
Correct Answer C. 97
Explanation In a parallelogram, opposite angles are congruent. Since angle J is opposite to the angle measuring 97 degrees, the measure of angle J is also 97 degrees.
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24.
In parallelogram ABCD, if AB = 8x - 2 and CD = 6x + 8, what is the length of AB?
Correct Answer 38
Explanation In a parallelogram, opposite sides are equal in length. So if AB is the same as CD, we can set them equal to each other and solve for x.
Given: AB = 8x - 2 CD = 6x + 8
Since AB is equal to CD: 8x - 2 = 6x + 8
Now, let's solve for x: 8x - 6x = 8 + 2 2x = 10 x = 5
Now that we have found the value of x, we can substitute it back into AB to find the length of AB:
AB = 8x - 2 AB = 8(5) - 2 AB = 40 - 2 AB = 38
Therefore, the length of AB in the parallelogram is 38 units.