Question

Find the value of each variable in the circle to the right . The dot represents the center of the circle . a= (Simplify your answer . Do not include the degree symbol in your answer .)

Answer 1

Given that the triangle is formed by the diameter of the triangle, we can deduct that angle b is 90°.

`b=90`

Then, we use the inscribed angle theorem to get

`a=(1)/(2)\cdot109=54.5`

Then, we use the interior angles theorem (triangle) to find the third acute angle

`\begin{gathered} a+b+x=180 \\ 54.5+90+x=180 \\ x=180-90-54.5 \\ x=35.5 \end{gathered}`

Now, we find arc c

`\begin{gathered} x=(1)/(2)\cdot c \\ 35.5=(1)/(2)\cdot c \\ c=2\cdot35.5 \\ c=71 \end{gathered}`

Hence, a = 54.5, b = 90, and c = 71.