Question

Consider the following three statements

Statement -1: When two lines intersect each other then the linear pair of angles are always equal to the vertically opposite angles.
Statement-2: If a ray stands on a line, then the sum of two adjacent angles so formed is ${180}^{\circ }$
Statement -3: In a right angle triangle between the other two angles one is obtuse and the other is acute.
Which of the following is correct.

• A. Statements 1 and 2 are true and statement 3 is false.
• B. All the Statements are true.
• C. Statements 1 and 3 are false and statement 2 is true.
• D. Statements 2 and 3 are true and statement 1 is false.

Answer 1

The correct option is C

Statements 1 and 3 are false and statement 2 is true.

Explanation for the correct option:

Correct option: (C)

Explanation for statement 1:

A pair of vertically opposite angles are always equal to itself. The sum of vertical angle and its adjacent is also a supplementary angles, which means the sum of both the angles is ${180}^o$.

Explanation for statement 2:

By linear property if a ray stands on a line, then the sum of two adjacent angles so formed is ${180}^o$.

Explanation for statement 3:

The sum of all the angles of a triangle is ${180}^o$. In a right angle triangle one angle is ${90}^o$. So, the sum of other two angles must be ${90}^o$i.e., complementary angle and we know that in complementary angle each angle must be acute angle.
Hence, Option (C) is the correct answer.