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:

Step1: Sum of triangle angles

The sum of angles in a triangle is \(180^\circ\).

Step2: Obtuse angle at B

Angle B is obtuse, so \(90^\circ < \angle B < 180^\circ\).

Step3: Remaining angles sum

\(\angle A + \angle C = 180^\circ - \angle B\). Since \(\angle B > 90^\circ\), this sum is less than \(90^\circ\).

Step4: Conclusion for angle A

Each of \(\angle A\) and \(\angle C\) must be less than \(90^\circ\) (as their sum is <90°).

Answer:

A. less than 90°.