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If ABCD is a cyclic parallelogram , then...

If ABCD is a cyclic parallelogram , then the `angleA` is .
यदि ABCD एक चक्रीय समांतर चतुर्भुज है, तो `angleA` क्या है?

A

`100^@`

B

`60^@`

C

`80^@`

D

`90^@`

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To solve the problem of finding the value of angle A in a cyclic parallelogram ABCD, we can follow these steps: ### Step 1: Understand the properties of a cyclic quadrilateral and a parallelogram. A cyclic quadrilateral is a four-sided figure where all vertices lie on a circle. In a cyclic quadrilateral, the opposite angles are supplementary. A parallelogram has opposite sides that are equal and opposite angles that are equal. ### Step 2: Identify the relationships between the angles. In a cyclic parallelogram ABCD: - Since ABCD is a parallelogram, we know that: - Angle A + Angle C = 180 degrees (opposite angles are supplementary). - Since ABCD is also cyclic, we know that: - Angle A = Angle C (opposite angles are equal). ### Step 3: Set up the equation using the properties. From the properties identified: - Let Angle A = x. - Then, Angle C = x (because they are equal). - According to the property of the parallelogram, we have: - x + x = 180 degrees. ### Step 4: Solve for angle A. Now, we can simplify the equation: - 2x = 180 degrees - x = 180 degrees / 2 - x = 90 degrees. ### Step 5: Conclusion. Thus, Angle A = 90 degrees. ### Final Answer: Angle A is 90 degrees. ---
To solve the problem of finding the value of angle A in a cyclic parallelogram ABCD, we can follow these steps: ### Step 1: Understand the properties of a cyclic quadrilateral and a parallelogram. A cyclic quadrilateral is a four-sided figure where all vertices lie on a circle. In a cyclic quadrilateral, the opposite angles are supplementary. A parallelogram has opposite sides that are equal and opposite angles that are equal. ### Step 2: Identify the relationships between the angles. In a cyclic parallelogram ABCD: - Since ABCD is a parallelogram, we know that: ...
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