Question

With reference to the figure below, consider the two statements:

Statement 1: The points A, B, and C will lie on a straight line if x + y = ${180}^{\circ }$.

Statement 2: The angle on a straight line is ${180}^{\circ }$.

• A. Both the statements are true and statement 2 is the correct explanation of statement 1.
• B. Both the statements are true and statement 2 is not the correct explanation of statement 1.
• C. Statement 1 is true and statement 2 is false.
• D. Statement 1 is false and statement 2 is true.

Answer 1

The correct option is A

Both the statements are true and statement 2 is the correct explanation of statement 1.

The angle on a straight line is ${180}^{\circ }$. Adjacent angles on a straight line add up to ${180}^{\circ }$.

Conversely, if adjacent angles add up to ${180}^{\circ }$ then the angles are on a straight line.

Hence, if x + y = ${180}^{\circ }$ , then A, B and C lie on a straight line.

Therefore, both the statements are true and statement 2 is the correct explanation of statement 1.