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The measure of the four successive angles of a quadrilateral are in the ratio 7 : 11 : 7 : 11. The quadrilateral is a ______.
- a)trapezium
- b)rectangle
- c)parallelogram
- d)square
Correct answer is option 'C'. Can you explain this answer?
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The measure of the four successive angles of a quadrilateral are in th...
Pair of opposite angles are equal in a parallelogram. Rectangle and square are also parallelogram but they have 90° angle at each corner.
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The measure of the four successive angles of a quadrilateral are in th...
Explanation:
Ratio of angles:
- The given ratio of the four successive angles of the quadrilateral is 7 : 11 : 7 : 11.
Sum of angles in a quadrilateral:
- In any quadrilateral, the sum of all four angles is always 360 degrees.
Calculating angle measurements:
- Let the angles be 7x, 11x, 7x, and 11x (in order) based on the given ratio.
- According to the ratio, the sum of the angles can be expressed as 7x + 11x + 7x + 11x = 360.
- Solving the equation, we get x = 15.
- Therefore, the angles are 105°, 165°, 105°, and 165°.
Identifying the quadrilateral:
- A quadrilateral with opposite angles being equal and the sum of all angles being 360 degrees is a parallelogram.
Conclusion:
- Hence, based on the ratio of the angles and the properties of a quadrilateral, the given quadrilateral is a parallelogram.
Ratio of angles:
- The given ratio of the four successive angles of the quadrilateral is 7 : 11 : 7 : 11.
Sum of angles in a quadrilateral:
- In any quadrilateral, the sum of all four angles is always 360 degrees.
Calculating angle measurements:
- Let the angles be 7x, 11x, 7x, and 11x (in order) based on the given ratio.
- According to the ratio, the sum of the angles can be expressed as 7x + 11x + 7x + 11x = 360.
- Solving the equation, we get x = 15.
- Therefore, the angles are 105°, 165°, 105°, and 165°.
Identifying the quadrilateral:
- A quadrilateral with opposite angles being equal and the sum of all angles being 360 degrees is a parallelogram.
Conclusion:
- Hence, based on the ratio of the angles and the properties of a quadrilateral, the given quadrilateral is a parallelogram.
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The measure of the four successive angles of a quadrilateral are in the ratio 7 : 11 : 7 : 11. The quadrilateral is a ______.a)trapeziumb)rectanglec)parallelogramd)squareCorrect answer is option 'C'. Can you explain this answer?
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