Question

Statements a and b are as given below:

a: If two lines intersect, then the vertically opposite angles are equal.

b: If a transversal intersects, two other lines, then the sum of two interior angles on the same side of the transversal is $180°$.

• A. Both $a$ and $b$ are true
• B. $a$ is true and $b$ is false
• C. $a$ is false and $b$ is true
• D. both $a$ and $b$ are false

Answer 1

The correct option is B

$a$ is true and $b$ is false

a: If two lines intersect, then the vertically opposite angles are equal.

b: If a transversal intersects, two other lines, then the sum of two interior angles on the same side of the transversal is $180°$.

When two lines intersect then the vertically opposite angles are always equal. When a transversal intersects, two other lines, then the sum of two interior angles on the same side of the transversal is $180°$ if and only if the two lines are parallel. The pair of angles are called as co-interior angles.

Hence, statement $a$ is true and $b$ is false, the B option is the correct answer.