SOLUTION: Write an indirect proof that two obtuse angles cannot for a linear pair.

Algebra ->  Geometry-proofs -> SOLUTION: Write an indirect proof that two obtuse angles cannot for a linear pair.       Log On


   

Question 835723: Write an indirect proof that two obtuse angles cannot for a linear pair.
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Let the two obtuse angles are ∠A and ∠B,

Assume they form a linear pair.

1. m∠A + m∠B = 180°   by definition of a linear pair.
2. m∠A > 90°          by definition of "obtuse angle"
3. m∠B > 90°          by definition of "obtuse angle"
   ----------
4. m∠A + m∠B > 180°  adding unequals to unequals in the same order gives
                      unequals in the same order.

Statement 4 contradicts statement 1.

Therefore obtuse angles ∠A  and ∠B cannot form a linear pair.

Edwin