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:
[tex]\begin{gathered} 180^{\circ}=90^{\circ}+52^{\circ}+z \\ 180^{\operatorname{\circ}}=142^{\operatorname{\circ}}+z \end{gathered}[/tex]We can substract 142° from both sides of this equation:
[tex]\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}[/tex]AnswerThen the answer is 38.