Answer to Question #102829 in Geometry for Dominique Miller

Question

can a base angle of an isosceles triangle be an obtuse angle

Answer 1

No, it can't have a obtuse base angle. The property of a triangle is that the sum of all angles in the triangle is equal to 180°. An isosceles triangle has two angles of the same measure at the base. So if it has an obtuse angle at the base, it has two obtuse base angles. The obtuse angles have the angles which are larger than a right angle and smaller than a straight angle (between 90° and 180°) .If 2 obtuse angles are added their sum will be more then 180°.So a triangle can not contain two obtuse angles and thus it can't have an obtuse angle at the base.