In the rectangle MPKH, the diagonals intersect at point O. The segment OA
August 30, 2021 | education|
In the rectangle MPKH, the diagonals intersect at point O. The segment OA is the height of the triangle MOP, ∠AOP = 15 °. Find OHK.
The triangle MPA is isosceles, since OP = OM as half the lengths of the diagonals of the MPKN rectangle, which are equal and are halved at point O. Then the height OA is also the bisector of the angle POM, which means that the angle POM = 2 * AOP = 2 * 15 = 30.
Angle KOH = POM as vertical angles at the intersection of the diagonals PH and MK, angle KOH = 30.
The KРН triangle is isosceles, then the angle OKH = OHK = (180 – KOH) / 2 = (180 – 30) / 2 = 75.
Answer: The value of the ONC angle is 75.
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