Question

triangle abc is an obtuse triangle with the obtuse angle at vertex b. angle a must be congruent to angle b greater than ( 90^{circ} ) less than ( 90^{circ} ) congruent to angle c

Explanation:

Step1: Recall the property of triangle angles

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

Step2: Analyze the given obtuse angle

Since angle \(B\) is obtuse (\(> 90^{\circ}\)), then angles \(A + C=180^{\circ}-B\). So \(A + C<90^{\circ}\).

Step3: Determine the nature of angle \(A\)

Since \(A + C<90^{\circ}\), both angle \(A\) and angle \(C\) must be less than \(90^{\circ}\).

Answer:

C. less than \(90^{\circ}\)