Question

Find the value of X and each arc measurex =mAD=mBC = mDC =mDBC=

Answer 1

The value of x can be calculated as,

`\begin{gathered} \text{ summation of angles = 360}^(\circ) \\ 12x+90+(2x+5)+(17x-14)=\text{ 360}^(\circ) \\ 31x+95-14=360 \\ 31x=360-81 \\ 31x=279^(\circ) \\ x=(279^(\circ))/(31) \\ x=9 \end{gathered}`
`\begin{gathered} \text{mAD }=\text{ 12x} \\ =12*9 \\ =108^(\circ) \end{gathered}`
`\begin{gathered} \text{mBC}=(2x+5)^(\circ) \\ =(2*9)+5 \\ =18+5 \\ =23^(\circ) \end{gathered}`
`\begin{gathered} \text{mDC }=(17x-14)^(\circ) \\ =(17*9)-14 \\ =153-14 \\ =139^(\circ) \end{gathered}`
`\begin{gathered} \text{mDBC }=\text{ }(2x+5)^(\circ)+(17x-14^{})^(\circ) \\ =23^(\circ)+139^(\circ) \\ =162^(\circ) \end{gathered}`