Step-by-step explanation
The sum of the three internal angles of a triangle is equal to 180°. For the triangle in the picture we have a 52° angle, a 90° right angle and an unknown angle z. Their sum must be equal to 180° so we get the following equation:
![\begin{gathered} 180^(\circ)=90^(\circ)+52^(\circ)+z \\ 180^{\operatorname{\circ}}=142^{\operatorname{\circ}}+z \end{gathered}]()
We can substract 142° from both sides of this equation:
![\begin{gathered} 180^{\operatorname{\circ}}-142^{\operatorname{\circ}}=142^{\operatorname{\circ}}+z-142^{\operatorname{\circ}} \\ z=180^{\operatorname{\circ}}-142^{\operatorname{\circ}} \\ z=38^(\circ) \end{gathered}]()
Answer
Then the answer is 38.