Question

Complete the indirect proof to show that two supplementary angles cannot both be obtuse angles. given: angle1 and angle2 are supplementary. prove: angle1 and angle2 cannot both be obtuse. assume that two supplementary angles can both be obtuse angles. so, assume that angle1 and angle2 are obtuse. then mangle1 > 90° (equation 1) and mangle2 > ° (equation 2) by the definition of angles. adding the two inequalities, mangle1 + mangle2 > ° (equation 3). however, by the definition of supplementary angles, mangle1 + mangle2 = (equation 4). so equation 3 contradicts the given information. this means the assumption is , and therefore angle1 and angle2 both be obtuse.

Answer 1

Two supplementary angles can never be both obtuse. To prove this, we use this example – consider two supplementary angles 60 degrees and 120 degrees. Sum of these two angles is 180 degrees. Here, the angle 120 degrees is an obtuse angle because obtuse angles are greater than 90 degrees. And since the angle 60 degrees is less than 90 degrees, it cannot be obtuse. Thus, the two supplementary angles cannot be both obtuse.