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Q1. If a circle is inscribed in a quadrilateral, what is the relationship between the lengths of the sides?
Solution:
For a quadrilateral to have an inscribed circle, the sum of the lengths of opposite sides must be equal.
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Q2. In a triangle, if two angles measure 45 degrees and 55 degrees, what is the measure of the third angle?
Solution:
The sum of the angles in a triangle is always 180 degrees. Therefore, the third angle = 180 - (45 + 55) = 80 degrees.
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Q3. In a cyclic quadrilateral, what is the relationship between the opposite angles?
Solution:
In a cyclic quadrilateral, the opposite angles are supplementary, meaning they add up to 180 degrees.
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Q4. If the radius of a circle is 7 cm, what is the circumference?
Solution:
The circumference of a circle is calculated using the formula 2πr. Thus, the circumference is 2π × 7 cm = 14π cm.
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Q5. If a regular hexagon has a side length of 6 cm, what is the perimeter of the hexagon?
Solution:
The perimeter of a regular hexagon is calculated as 6 times the side length. Therefore, perimeter = 6 × 6 cm = 36 cm.
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Q6. If the radius of a circle is 7 cm, what is the circumference of the circle?
Solution:
The circumference of a circle is calculated using the formula 2πr. Therefore, circumference = 2π × 7 cm = 14π cm.
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Q7. If a regular hexagon has a side length of 3 cm, what is the perimeter of the hexagon?
Solution:
The perimeter of a regular hexagon is calculated as 6 times the side length. Therefore, perimeter = 6 × 3 cm = 18 cm.
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Q8. In a parallelogram, if one angle measures 70 degrees, what is the measure of the opposite angle?
Solution:
In a parallelogram, opposite angles are equal. Therefore, if one angle is 70 degrees, the opposite angle is also 70 degrees.
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