ANSWER
The larger angle is 71° and the smaller angle is 19°.
EXPLANATION
Let the first angle be x.
Let the second angle be y.
The two angles add up to 90 degrees. This implies that:
[tex]x+y=90[/tex]The difference between the two angles is 52. This implies that:
[tex]x-y=52[/tex]Now, we have a system of simultaneous equations:
[tex]\begin{gathered} x+y=90 \\ x-y=52 \end{gathered}[/tex]To solve by elimination, add the two equations to eliminate y:
[tex]\begin{gathered} x+y+x-y=90+52 \\ x+x+y-y=142 \\ 2x=142 \\ x=\frac{142}{2} \\ x=71\degree \end{gathered}[/tex]To find the value of y, substitute the value of x into the first equation:
[tex]\begin{gathered} 71+y=90 \\ \Rightarrow y=90-71 \\ y=19\degree \end{gathered}[/tex]Hence, the larger angle is 71° and the smaller angle is 19°.
