Given that the triangle is formed by the diameter of the triangle, we can deduct that angle b is 90°.
[tex]b=90[/tex]
Then, we use the inscribed angle theorem to get
[tex]a=\frac{1}{2}\cdot109=54.5[/tex]
Then, we use the interior angles theorem (triangle) to find the third acute angle
[tex]\begin{gathered} a+b+x=180 \\ 54.5+90+x=180 \\ x=180-90-54.5 \\ x=35.5 \end{gathered}[/tex]
Now, we find arc c
[tex]\begin{gathered} x=\frac{1}{2}\cdot c \\ 35.5=\frac{1}{2}\cdot c \\ c=2\cdot35.5 \\ c=71 \end{gathered}[/tex]
Hence, a = 54.5, b = 90, and c = 71.
