The diagonal divides the corner of the rectangle into two corners, one of which is 10 degrees larger than the other.
| July 3, 2021 | education
The diagonal divides the corner of the rectangle into two corners, one of which is 10 degrees larger than the other. Find an acute angle between the diagonals of the triangle.
Let the angle OAD = X0, then the angle AOB = (X + 10) 0.
Since the angle BAD = 90, then X + X + 10 = 90.
2 * X = 80.
X = OAD = 80/2 = 40.
AOB = 40 + 10 = 50.
Triangle AOB is isosceles, OA = OB as half the diagonals of the rectangle, then the angle AOB = (180 – 50 – 50) = 80.
Answer: The acute angle between the diagonals is 80.
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