Question

Consider the following three statements
Statement -1 : Difference between the sum of supplementary angles and the sum of complementary angles is a right angle.
Statement -2 : If a transversal intersect two parallel lines, then the sum of each pair of interior angles on the same side of the transversal is double of right angle.
Statement -3: The exterior angle of a triangle is equal to the sum of three interior angles.
Which of the following is correct

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

Answer 1

The correct option is A

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

Explanation for the correct option:

Correct option: (A)

Explanation for statement 1:

Sum of supplementary angle = ${180}^o$

Sum of complementary angle = ${90}^o$

Difference = ${180}^o-{90}^o={90}^o$.

Hence, Difference between the sum of supplementary angles and the sum of complementary angles is a right angle.

Explanation for statement 2:

A transversal intersect two parallel lines

Sum of interior angle on the same side of transversal = ${180}^o$= $2\times {90}^o$= $2($Right angle).

Hence, If a transversal intersect two parallel lines, then the sum of each pair of interior angles on the same side of the transversal is double of right angle.

Explanation for statement 3:

The exterior angle of a triangle is equal to the sum of two interior angles.
Hence, option (A) is the correct answer.