Answer:
m∠N = 32°
NQ = 106°
When finding inscribed angles like ∠N with the intercepted arc, the equation is ∠N=1/2MP. (Inscribed angles are always half the degree of the arc length.) Plug in the corresponding value to get ∠N=1/2(64) to get 32°. When finding the angle of the intercepted arc with inscribed angles like NQ, the equation is NQ=2(∠P). Plug in the corresponding value to get 2(53) to get 106°.
Since the side which measures 10 is a vertical projection of the hipotenuse x on a 20 degree angle:
10 = x*sin(20°)
x = 29.238044
Since we have to round to the nearest hundreth:
x = 29.24 m
