Question

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

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

Statement II: If the angle between two lines is ${180}^{\circ }$, then all the points on both the lines lie on a straight line.

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

Answer 1

The correct option is A

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

If three or more points lie on same line, they are called collinear points. When the sum of $\angle$ABD and $\angle$DBC is equal to ${180}^{\circ }$ i.e. x+y= ${180}^{\circ }$, (sum of two adjacent angles is ${180}^{\circ }$), then they are called as linear pair of angles. Hence the three points lie in the same line and are collinear. So both the statements are true and statement 2 is the correct explanation of statement 1.