What's the measure of the angle $ \measuredangle OBH$?

Question

For reference: In an acute triangle ABC, H is the orthocenter and O is the circumcenter. Find the $ \measuredangle OBH, if ~\measuredangle A - \measuredangle C=24^o $

My progresss: I made the drawing and the following relationships

$\measuredangle AOC = 2(\alpha +\theta)\\ \triangle AOB ~and ~\triangle BOC~and \triangle AOC~are ~isosceles\\ \measuredangle DAO = 90^o -(\alpha+\theta)\implies \measuredangle ABE = \theta\\ \measuredangle DAB=90-\theta $

Answer 1

Your diagram already shows it: $\angle OBH$ is the red angle;

$$\angle OBH = \alpha - \theta$$

And from the given,

$$\alpha - \theta = \angle A - \angle C = 24^\circ$$