Triangle ABC is an obtuse triangle with the obtuse angle at vertex B. Angle A must 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.