Question 127556

Use indirect reasoning to explain why a triangle cannot have more than one obtuse angle.

First, assume that a triangle does have {{{more }}}{{{than }}}{{{one }}}{{{obtuse }}}{{{angle}}}. 

The measure of an obtuse angle is greater than {{{90}}} degrees. Hence, the sum of the measures of {{{two }}}{{{obtuse }}}angles is {{{greater}}} than {{{180}}} degrees, and the sum of the measures of {{{three }}}{{{obtuse}}} angles is greater that {{{270}}} degrees. 

The sum of the angles of a triangle, however, {{{equals }}}{{{180 }}}degrees. 

Therefore, {{{only}}}{{{ one}}}{{{ angle}}} in a triangle can be {{{obtuse}}}.