Question

I need help i dont know how to solve it

Answer 1

mFJH = 210º

Step-by-step explanation

The measure of an arc is twice the measure of the inscribed angle subteded by it:

`\text{mFJH}=2m\angle FGH`

First we have to find x:

`17x-28=2(6x+21)`

Apply distributive property of addition on the right side:

`\begin{gathered} 17x-28=2\cdot6x+2\cdot21 \\ 17x-28=12x+42 \end{gathered}`

Now we have to get the x together on the same side of the equation. To do that we have to subtract 12x from both sides:

`\begin{gathered} 17x-12x-28=12x-12x+42 \\ 5x-28=42 \end{gathered}`

Now, add 28 to both sides:

`\begin{gathered} 5x-28+28=42+28 \\ 5x=70 \end{gathered}`

And finally divide both sides by 5:

`\begin{gathered} (5x)/(5)=(70)/(5) \\ x=14 \end{gathered}`

Now, with x = 14, we just have to replace it into the expression for the measure of arc FJH:

`\begin{gathered} \text{mFJH}=17x-28 \\ \text{mFJH}=17\cdot14-28 \\ \text{mFJH}=238-28 \\ \text{mFJH}=210 \end{gathered}`

The measure of arc FJH is 210º