Question

Example 11 on page 4

Answer 1

We know that

`m\angle\text{BYD}+m\angle\text{DYO}=m\angle\text{BYO}`

Then, let's put the respective equation and values:

`\begin{gathered} m\angle\text{BYD}+m\angle\text{DYO}=m\angle\text{BYO} \\ \\ (x+4)+(3x-8)=68\degree \end{gathered}`

Now we solve the equation for x

`\begin{gathered} (x+4)+(3x-8)=68 \\ \\ x+4+3x-8=68 \\ \\ x+3x=68+8-4 \\ \\ 4x=72 \\ \\ x=18 \end{gathered}`

Therefore the value of x is 18.

Now we have the value of x we can find out m∠DYO:

`\begin{gathered} m\angle\text{DYO}=3x-8 \\ \\ m\angle\text{DYO}=3\cdot(18)-8 \\ \\ m\angle\text{DYO}=54-8 \\ \\ m\angle\text{DYO}=46\degree \end{gathered}`

Hence, m∠DYO = 46°

The final answers are

x = 18

m∠DYO = 46°