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The sum of angles of a rhombus is-...

The sum of angles of a rhombus is-

A

`360^(@)`

B

`180^(@)`

C

`156^(@)`

D

`356^(@)`

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The correct Answer is:
To find the sum of the angles of a rhombus, we can follow these steps: ### Step-by-Step Solution: 1. **Understand the Properties of a Rhombus**: A rhombus is a type of quadrilateral where all four sides are of equal length. The opposite angles are equal, and the adjacent angles are supplementary (they add up to 180 degrees). 2. **Identify the Angles**: Let's denote the angles of the rhombus as A, B, C, and D. According to the properties of a rhombus: - Angle A = Angle C - Angle B = Angle D 3. **Set Up the Equation for the Sum of Angles**: The sum of the interior angles of any quadrilateral is always 360 degrees. Therefore, we can write: \[ A + B + C + D = 360^\circ \] 4. **Substituting the Equal Angles**: Since A = C and B = D, we can substitute: \[ A + B + A + B = 360^\circ \] This simplifies to: \[ 2A + 2B = 360^\circ \] 5. **Dividing by 2**: To simplify further, divide the entire equation by 2: \[ A + B = 180^\circ \] 6. **Conclusion**: Therefore, the sum of the angles of a rhombus is: \[ A + B + C + D = 360^\circ \] ### Final Answer: The sum of angles of a rhombus is **360 degrees**.
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