Question

Can a right triangle also be obtuse? Explain your reasoning.

yes; By the Exterior Angle Theorem, If one of the exterior angles is obtuse, then it is possible for one of the two nonadjacent interior angles to be obtuse.

yes; A right angle measures 90∘∘. By the Corollary to the Triangle Sum Theorem, the other two angles are complementary. So, one of those angles can be obtuse as long as the sum of the two angles is 90∘∘.

no; By the Corollary to the Triangle Sum Theorem, the angles in a right triangle that are not right angles are acute and complementary.

no; By the Exterior Angle Theorem, if one of the exterior angles is obtuse, the two nonadjacent interior angles will each have half the measure of the exterior angle, so they will both be ac

Answer 1

I don’t think so, because in order for it to be obtuse, it has to be more than 90 degrees, but a right triangle is 90 degrees exact, so it can’t be obtuse. Hope this helps :)

Answer 2

No.By the Corollary to the Triangle Sum Theorem, the angles in a right triangle that are not right angles are acute and complementary.

Explanation:

In a triangle sum of all three angles is 180 degrees

Hence when one angle is 90 degrees, other two angles should add up to 90 degrees.

Hence the triangle cannot be obtuse. And two complementary positive angles cannot be obtuse.

Hence we get

No.By the Corollary to the Triangle Sum Theorem, the angles in a right triangle that are not right angles are acute and complementary.