Question

Find the value of X and each arc measurex =mDE =mEF = mDFG =

Answer 1

Arc EF + arc FG = 180 ( Reason: GE is a straight line)

`\begin{gathered} x-3+12x-25=180 \\ 13x-28=180 \\ 13x=180\text{ + 28} \\ 13x=208 \\ \text{Divide both sides by 13},\text{ we get,} \\ x\text{ =}(208)/(13)=16 \end{gathered}`

Arc DE = Arc GF = 12x - 25 = 12(16) - 25 = 192 - 25 = 167 degrees

Arc EF = x -3 = 16 - 3 = 13 degrees

Arc DFG = arc DE + arc EF + arc FG = 167 + 13 + 167 = 347 degrees