Question

Which statement is true about this argument?

Answer 1

Answer with explanation:

→The statement is always true that,if two angles form a linear pair ,then they are supplementary.

→Linear pair Axiom states that,if a ray cuts a line ,then sum of adjacent angles on the same side of ray is 180°.

→ The Meaning of term supplementary angles is that, sum of two angles should be equal to 180°.

→If two angles, ∠a And ∠b forms , linear pair ,then ,∠a+∠b=180°, that is if sum of two angles is 180°,it means they are supplementary also.

→But , if sum of two angles is 180°,it does not guarantee that, they will form Linear Pair.

I have illustrated this concept with the help of ,lines, angles, ray,and Transversal .

→So,yes, If two angles form a linear pair,sum of their measures will be 180°,but if two angles are supplementary, it does not guarantee that they will form a linear Pair.

Answer 2

Answer:

The argument is true by the law of syllogism

Explanation:

Law of syllogism states that for a valid argument form which is a syllogism having a conditional statement for one or both of its premises.

Premises:

1. If p , then q

2. if q, then r

Conclusion: if p, then r.

Let p be the statement "two angles form a linear pair",

let q be the statement "they are supplementary"  and

let r be the statement "the sum of their measures is 180°"

If p, then q

if q,  then r

then by the Law of syllogism statement , conclusion if q then r is true,

i,e If two angles form a linear pair, then the sum of their measures is $180^{\circ}$.