Work out the size of angle m.

Step 1: Identify the shape and its properties. The given shape is a quadrilateral, which is a polygon with four sides. The sum of the interior angles of any quadrilateral is $360^\circ$.

Step 2: Identify the known angles. The diagram shows three known interior angles: • One angle is $86^\circ$. • Another angle is $67^\circ$. • The square symbol indicates a right angle, which is $90^\circ$. • The fourth angle is $m$.

Step 3: Set up the equation for the sum of the interior angles. $86^\circ + 67^\circ + 90^\circ + m = 360^\circ$

Step 4: Add the known angles. $243^\circ + m = 360^\circ$

Step 5: Solve for $m$ by subtracting $243^\circ$ from both sides. $m = 360^\circ - 243^\circ$ $m = 117^\circ$

Final Answer $\boxed{117^\circ}$