Q:

Which statement is true about this argument? Premises: If two angles form a linear pair, then they are supplementary. If two angles are supplementary, then the sum of their measures is 180°. Conclusion: If two angles form a linear pair, then the sum of their measures is 180°.

Accepted Solution

A:
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.