In the rectangle, MPOK intersect at point C. Find the angle between the diagonals if the PMO angle is 40 degrees.
| September 5, 2021 | education
In the rectangle, the diagonals are equal and at the point of their intersection they are divided in half, then СР = СМ = СK = СО. So the PCM triangle is isosceles, then the angle MPC = РMO = PMC = 40.
Since the sum of the interior angles of the triangle is 180, the angle PCM = (180 – 40 – 40) = 100.
The MCК angle is adjacent to the PCM angle, and since the sum of adjacent angles is 180, the MCК angle = 180 – 100 = 80.
Answer: The angles between the diagonals are 80 and 100.
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