1. **Problem Statement:** We are given a figure with angles and lines, and two statements to verify: - Statement I: The value of $x$ is 130°. - Statement II: If lines $p \parallel q$, then the value of $a$ is 50°. 2. **Analyzing Statement I:** - The large triangle has angles 80°, 30°, and 20°. - The sum of angles in any triangle is always 180°. - Check if $x = 130°$ fits the triangle angle sum rule. 3. **Triangle Angle Sum Rule:** $$\text{Sum of angles} = 180°$$ 4. **Check the given angles:** $$80° + 30° + 20° = 130°$$ - This sum is 130°, which is less than 180°. - Therefore, the angle labeled $x$ cannot be 130° because the triangle's angles must sum to 180°. - Statement I is **incorrect**. 5. **Analyzing Statement II:** - Lines $p$ and $q$ are parallel. - A transversal crosses these lines creating angles 120°, 50°, $a$, and another 50°. - When two lines are parallel, alternate interior angles are equal. 6. **Using Parallel Lines Property:** - The angle $a$ corresponds to the alternate interior angle of 50°. - Therefore, $a = 50°$. - Statement II is **correct**. 7. **Conclusion:** - Statement I is incorrect. - Statement II is correct. **Final answer:** Option B: Statement-I is incorrect and Statement-II is correct.