From the statement of the problem, we know that:
[tex]m(\angle4)=18^{\circ}\text{.}[/tex]
From the diagram, we see that:
1) ∠1 and ∠4 are complementary angles, so they sum up 90°:
[tex]\begin{gathered} m\mleft(\angle1\mright)+m\mleft(\angle4\mright)=90\degree \\ m\mleft(\angle1\mright)=90\degree-m\mleft(\angle4\mright), \\ m(\angle1)=90\degree-18^{\circ}=72^{\circ}\text{.} \end{gathered}[/tex]
2) ∠4, ∠3 and a right angle are inner angles of a triangle, so they must sump up 180°:
[tex]\begin{gathered} m(\angle4)+m(\angle3)+90^{\circ}=180^{\circ}\text{.} \\ m(\angle3)=180^{\circ}-90^{\circ}-m(\angle4), \\ m(\angle3)=180^{\circ}-90^{\circ}-18^{\circ}=72^{\circ}\text{.} \end{gathered}[/tex]
3) ∠3 and ∠2 are complementary angles, so they sum up 90°:
[tex]\begin{gathered} m(\angle3)+m(\angle2)=90^{\circ}, \\ m(\angle2)=90^{\circ}-m(\angle3), \\ m(\angle2)=90^{\circ}-72^{\circ}=18^{\circ}\text{.} \end{gathered}[/tex]
Answer
c. m(∠1) = 72°, m(∠2) = 18°, m(∠3) = 72°.
