Answer: [tex]m\angle R=77.2\°[/tex]
Step-by-step explanation:
For this exercise you need to use an Inverse Trigonometric Function called "Arctangent".
By definition:
[tex]\alpha =arctan(\frac{opposite}{adjacent})[/tex]
You must observe carefully the triangle PQR shown in the picture attached.
In this case you can identify that:
[tex]\alpha=m\angle R\\\\opposite=PQ=8\\\\adjacent=QR=3[/tex]
Therefore, knowing those values you can substitute them into [tex]\alpha =arctan(\frac{opposite}{adjacent})[/tex] , as following:
[tex]m\angle R=arctan(\frac{PQ}{QR})\\\\m\angle R=arctan(\frac{8}{3})[/tex]
Finally, evaluating, you get that the measure of the angle R is the following:
[tex]m\angle R=77.15\°[/tex]
Rounding to the nearest tenth:
[tex]m\angle R\approx77.2\°[/tex]
