Question 1176856
Prove this using indirect proof in two-column form.
Given: {{{MP}}} ⊥ ̅{{{NO}}}
Prove: ∠ {{{NPM}}} is not a straight angle


statement........................................................reason


1) ∠{{{NPM }}}is a straight angle	...........1) Assumpe opposite

2) m∠{{{NPM = 180}}}°....................	2) Definition of a striaght angle

3){{{MP }}}⊥ ̅{{{NO}}}	....................................3) Given

4) ∠{{{NPM}}} is a right angle.................	4) definition of perpendicular lines

5) m ∠{{{NPM = 90}}}}°....................	5) definition of a right angle

6) m ∠{{{NPM}}} is not a straight angle................	contradiction of steps 2 and 5

7) ∠{{{NPM}}} is not a straight angle.....................	due to the contradiction between 2 and 5, we know that the assumption that WE INTRODUCED
in the first step (∠{{{NPM}}} is a straight angle) is {{{false}}}. 
Therefore, the opposite must be {{{true}}}: ∠ {{{NPM }}} is {{{not}}} a straight angle