In the ABCD diamond, the ABC angle is 126 degrees. Find the angle ACD.
| May 27, 2021 | education
One of the properties of a rhombus is that the opposite corners of the rhombus are equal.
In this problem, ∠ABC and ∠ADC are opposite, which means that ABC = ∠ADC = 126 °.
By the definition of a rhombus, all its sides are equal, that is, DА = DC, it follows that the triangle ACD is isosceles and ∠АСD = ∠САD.
Since the sum of the angles of the triangle is 180 °, ∠ADС = 126 ° and ∠АСD = ∠САD, then:
∠АСD = (180 – 126) / 2 = 27 °.
Answer: 27 °.
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