Question

What are the values of a b r and s

Answer 1

Step 1

Given:

`\begin{gathered} l_1||l_2 \\ m\angle a=13y \\ m\angle b=31y+4 \\ m\angle r=30x+40 \\ m\angle s=130x\text{ -160} \end{gathered}`

Required; To find the values of a,b,r and s.

Step 2

Find the values of a,b,r and s.

`m\angle b=\text{ 180 - m}\angle a\text{ ----( sum of angles on a striaght line)}`
`\begin{gathered} 31y\text{ + 4 =180 -13y} \\ 31y+13y\text{ = 180 -4} \\ 44y=\text{ 176} \\ (44y)/(44)=(176)/(44) \\ y=\text{ 4} \end{gathered}`
`\begin{gathered} m\angle a=13(4)=52^o \\ m\angle b\text{ = 31(4)+4}=124+4=128^o \\ \end{gathered}`
`\begin{gathered} m\angle r=m\angle s(\text{ corresponding angles ar }equal) \\ 30x+40=130x-160 \\ 40+160=130x-30x \\ 200=100x \\ (100x)/(100)=(200)/(100) \\ x=2 \end{gathered}`
`\begin{gathered} m\angle r=30(2)+40=60+40=100^o^{} \\ m\angle s=130(2)-160=260-160=100^o \end{gathered}`