The degree measure of one of the corners of the rhombus is 140 °. Find the degree measure of the angle formed
| March 20, 2021 | education
The degree measure of one of the corners of the rhombus is 140 °. Find the degree measure of the angle formed by the side of the rhombus and its diagonal drawn from the top of the acute angle.
The sum of the inner angles of a rhombus is 360, and its opposite angles are equal to each other.
∠BCD = ∠BAD = 140.
∠ABS = ∠ADС.
Then: ∠ABS = ∠ ADC = (360 – 140 – 140) / 2 = 80/2 = 40.
Since the diagonals of the rhombus divide the angles at the vertex in half, then ∠СDО = ∠ADС / 2 = 40/2 = 20.
Answer: The angle between the side of the rhombus and the diagonal is 20.
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