In the rhombus ABCD, the angle ACD is 43 degrees, find the angle ABC.
| September 21, 2021 | education
Diagonals AC and BD of rhombus ABCD are the bisectors of its angles.
Means: ∠ ACD = ∠ ACB = 43 °.
Angle С is equal to the sum of angles ACD and ABC: ∠ С = ∠ ACD + ∠ ACB = 43 ° + 43 ° = 86 °.
A rhombus is a parallelogram, so the sum of its two adjacent angles is 180 °.
∠ С + ∠ ABC = 180 °.
Hence:
∠ ABC = 180 ° – ∠ С = 180 ° – 86 ° = 94 °.
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