In rhombus ABCD, the height of AK crosses the diagonal BD at point E, ADE = 40 °. Find the value of the angle EAC.
| March 2, 2021 | education
Since the diagonal of the rhombus divides the angle at the apex in half, the angle ADC = 2 * ADE = 2 * 40 = 80.
The opposite angles of the rhombus are equal, then the angle ABC = 80. In the right-angled triangle ABK, the angle BAK = 180 – 90 – 80 = 10.
The sum of the adjacent angles of the rhombus is 180, then the angle BAD = 180 – 80 = 100, and the angle BAO = BAD / 2 = 100/2 = 50.
Then the angle EAC = BAO – BAE = 50 – 10 = 40.
Answer: The EAC angle is 40.
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