In a triangle ABC, if angle B is obtuse, what types of angles can angles A and C be?
Angle A must be acute.
Both angle A and C must be acute. The sum of the angles in a triangle is 180°.
An obtuse angle is more than 90°, so the sum of the remaining 2 angles has to be less than 90°.
Note that it is impossible to have:
2 right angles in a triangle, because
#90° + 90° = 180#° and the third angle still needs to be added.
1 obtuse and 1 right angle in a triangle, their sum is more than 180°
2 obtuse angles in a triangle, their sum is more than 180°
It is possible to have an obtuse-angled isosceles triangle, but the vertex angle must be obtuse and the equal base angles will be acute.