1. The problem is to understand and solve questions related to lines and angles for class 9th. 2. Important formulas and rules include: - The sum of angles on a straight line is $180^\circ$. - Vertically opposite angles are equal. - Angles in a triangle sum to $180^\circ$. - Corresponding angles are equal when a transversal cuts parallel lines. 3. Example question: Find the value of $x$ if two lines intersect and form angles $3x$ and $2x + 30^\circ$ which are vertically opposite. 4. Since vertically opposite angles are equal, set up the equation: $$3x = 2x + 30$$ 5. Subtract $2x$ from both sides: $$3x - \cancel{2x} = 2x + 30 - \cancel{2x}$$ $$x = 30$$ 6. So, the value of $x$ is $30$ degrees. 7. This method applies to various problems involving lines and angles by using the properties and formulas stated above.