In a rectangle mpkn, the diagonals intersect each other at point o. a line segment
oa
is an altitude of δmop,
m∠aop = 15°. find m∠onk.

It will really be helpful in your solution if you draw the rectangle, its diagonal and the altitude of ΔMOP. 

By doing so, you will find that ∠MOP is equal to twice m∠AOP and that is equal to 30°. Then, m∠MOP is a vertical angle of m∠NOK which means that they are equal. Therefore, m∠NOK is also 30°. 

We know that the sum of the angles of a triangle is equal to 180°.
                m∠NOK + m∠OKN + m∠ONK = 180°
And that m∠OKN = m∠ONK
so,
                 m∠NOK + 2m∠ONK = 180°
Substituting,
                 30° + 2m∠ONK = 180°
Hence,
                        m∠ONK = 75°

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