the measure of two adjacent angles of a quadrilateral are 110 degree and 50 degree and other two acute angles are equal. find the measureof each angles

Please check your question once because as per my interpretation other two angles will not be acute if they are equal.

Let each of other two angles of a quadrilateral be x.
Measure of adjacent angles are $110°$ and 50$°$.
We know that the sum of angles of quadrilateral is 360$°$.
So; $x+x+110°+50° = 360°$
$$\begin{gathered} \Rightarrow 2x+160° = 360° \\ \Rightarrow 2x = 360°-160° = 200° \\ \Rightarrow x = \frac{200°}{2}= 100° \end{gathered}$$
Therefore four angles of quadrilateral are $110°$, 50$°$,100$°$ and 100$°$