Given:
A figure is given.
Required:
Find the value of x and y.
Explanation:
Two lines are intersecting each other at a point so the opposite angles will be vertically opposite angles.
The vertically opposite angles are equal so
[tex]\begin{gathered} (7x+15)\degree=(3x+85)\degree \\ 7x\degree+15\degree=3x\degree+85\degree \\ 7x\degree-3x\degree=85\degree-15\degree \\ 4x\degree=70\degree \\ x=17.5\degree \end{gathered}[/tex]
We know that the sum of linear angles is 18 degrees.
[tex]2y\degree+(7x+15)\degree=180\degree[/tex]
Substitute the value of x in the equation.
[tex]\begin{gathered} 2y\degree+(7\times17.5+15)=180\degree \\ 2y\degree+137.5\degree=180\degree \\ 2y\degree=180-137.5\degree \\ 2y\degree=42.5\degree \\ y=21.25\degree \end{gathered}[/tex]
So the values are
[tex]\begin{gathered} x=17.5\degree \\ y=21.25\degree \end{gathered}[/tex]
Final Answer:
Option b is the correct answer.
