Triangle abc is an obtuse triangle with the obtuse angle at vertex b. angle a must be less than 90°. greater than 90°. congruent to angle b. congruent to angle c.

The Angle A of the obtuse triangle ABC must be less than 90°

First option: less than 90°

Solution

Triangle ABC is an obtuse triangle with the obtuse angle at vertex B, this means that the angle at vertex B must be greater than 90° (definition of obtuse angle):

Angle at vertex B > 90°

We know that the sum of the interior angles of any triangle must be equal to 180°, then in this case:

Angle A + Angle B + Angle C = 180°

Subtracting Angle B both sides of the equation:

Angle A + Angle B + Angle C - Angle B = 180° - Angle B

Angle A + Angle C = 180° - Angle B

Like the Angle B is greater than 90°, 180°-Angle B is less than 90°:

180°-Angle B < 90°

Angle A + Angle C = 180° - Angle B < 90°

Angle A + Angle C < 90°

The sum of the angles A and C must be less than 90°, and each of them (Angle A and Angle C) must be less than 90° too, then:

Angle A must be less than 90°