# In a triangle ABC, if angle B is obtuse, what types of angles can angles A and C be?

Dec 12, 2016

Angle A must be acute.

#### Explanation:

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.