Question

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.

Explanation:

In a triangle, the sum of interior angles is \(180^\circ\). An obtuse angle is greater than \(90^\circ\) but less than \(180^\circ\). Since triangle \(ABC\) has an obtuse angle at \(B\), \(\angle B>90^\circ\). Let \(\angle A + \angle B+\angle C = 180^\circ\). If \(\angle B>90^\circ\), then \(\angle A+\angle C=180^\circ - \angle B<90^\circ\). So both \(\angle A\) and \(\angle C\) must be less than \(90^\circ\) (acute angles). Also, there's no reason for \(\angle A\) to be congruent to \(\angle B\) (as \(\angle B\) is obtuse and \(\angle A\) is acute) or to \(\angle C\) (unless it's an isosceles triangle, but the problem doesn't state that). So \(\angle A\) must be less than \(90^\circ\).

Answer:

less than \(90^\circ\)