Arc RE subtends quarter of a circle, 90 degrees.
Arc RE has the same measure as the central angle it subtends, so
Arc RE = 90°
Similarly, Arc IE is equal to 15°.
Looking at the figure, we can write,
[tex]ArcRE=ArcIR+ArcIE[/tex]Putting the information we know, let's find the measure of Arc IR:
[tex]\begin{gathered} ArcRE=ArcIR+ArcIE \\ 90=ArcIR+15 \\ ArcIR=90-15 \\ ArcIR=75\degree \end{gathered}[/tex]Answer[tex]75\degree[/tex]