To answer this question, we need to understand the properties of each quadrilateral.

Option A) Trapezium - In a trapezium, only one pair of opposite sides is parallel. Therefore, option A does not satisfy the condition that the opposite sides are parallel, so it is incorrect.

Option B) Rhombus - In a rhombus, all four sides are equal in length, so both pairs of opposite sides are the same length. However, a rhombus does not necessarily have opposite angles that are equal, so option B is incorrect.

Option C) Parallelogram - In a parallelogram, both pairs of opposite sides are parallel, so it satisfies condition b). Additionally, the opposite angles in a parallelogram are equal, so it satisfies condition c) as well. However, a parallelogram does not necessarily have all sides of equal length, so option C does not satisfy condition a).

Option D) Kite - In a kite, the opposite sides are not parallel, so option D does not satisfy condition b). Therefore, option D is incorrect.

Therefore, the correct answer is option C) Parallelogram. It is the only quadrilateral in which both pairs of opposite sides are parallel and the opposite angles are equal.

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• Wrong explanation

To answer this question, let's break down the information given:

The Smith family has:

• Mother
• Father
• 7 daughters
• Each daughter has 1 brother

From this information, we can deduce that there is only 1 brother for all the daughters. Therefore, there is only 1 son in the family.

To calculate the total number of people in the family, we add up the number of family members:

• Mother: 1
• Father: 1
• 7 daughters: 7
• 1 son: 1

So, the total number of people in the family is 1 + 1 + 7 + 1 = 10.

Therefore, the correct answer is option C) 10.

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• Wrong explanation

To answer this question, let's analyze the given sequence:

1 = 5 2 = 25 3 = 125 4 = 625

Looking at the pattern, we can see that each number in the sequence is obtained by raising the corresponding number to the power of 5.

So, 5 raised to the power of 1 is 5, 5 raised to the power of 2 is 25, 5 raised to the power of 3 is 125, and 5 raised to the power of 4 is 625.

Therefore, the next number in the sequence would be 5 raised to the power of 5, which is 3125.

Hence, the correct answer is option A) 3125.

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• Wrong explanation