Calculate the degree measures of the angles of the rhombus ABCD if the perimeter is 24cm and AC = 6cm.

univerkov | September 14, 2021 | education

1. Р – perimeter.

2. Each side of the rhombus = P: 4 = 24: 4 = 6 centimeters.

3. Triangle. ABC is equilateral. Each of its sides is 6 centimeters, and each of the angles is 60 °.

4. Therefore, ∠В = 60 °.

5. In a rhombus, the angles opposite each other (opposite) are equal:

∠В = ∠Д = 60 °.

6. ∠А = 180 ° – ∠В = 180 ° – 60 ° = 120 °.

∠А = ∠С = 120 °.

Answer: ∠В = ∠Д = 60 °, ∠А = ∠С = 120 °.

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