Answer:
70.52 degrees
Step-by-step explanation:
To find the angles, we must first find the lengths of each side of the triangle. Adding up the respective radii, we can see that
XY = 5+4 = 9 CM
XZ = 6+5 = 11 CM
ZY = 4+6 = 10 CM
Now we can apply the cosine rule
[tex]C\:=\:\sqrt{A^2+B^2-2ABcosx}[/tex]
We need to rearrange the rule to solve for x, our missing angle
[tex]x\:=\:cos^{-1}\left(\frac{a^2+b^2-c^2}{2ab}\right)[/tex]
solving for our unknown angle:
[tex]x\:=\:cos^{-1}\left(\frac{9^2+10^2-11^2}{2\cdot 9\cdot 10}\right)[/tex]
[tex]x\:=\:70.52^{\circ }[/tex]
Therefore angle YXZ is 70.52 degrees
