Answer: [tex]53^{\circ}[/tex]
Step-by-step explanation:
In the given figure , we have a triangle having sides , 18 , 17 and 20.
Law of cosines :-
[tex]a^2=b^2+c^2-2bc\cos(A)[/tex], where a, b and c are the sides of the triangle and A is the angle opposite to side a.
Since angle Q is opposite to side MN with measure 17 .
Put a= 17 , b=18 and c=20 in the equation , we get
[tex]17^2=18^2+20^2-2(18)(20)\cos(Q)\\\\\Rightarrow\ 720\cos(Q)=18^2+20^2-17^2\\\\\Rightarrow\ 720\cos(Q)=435\\\\\Rightarrow\ \cos(Q)=\dfrac{435}{720}\\\\\Rightarrow\ \angle{Q}=\cos^{-1}(\dfrac{435}{720})=0.92207665\text{radian}\\\\\Rightarrow\angle{Q}=0.92207665\times\dfrac{180}{\pi}\approx53^{\circ}[/tex]
