Question

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

Explanation:

Step1: Recall the sum of angles in a triangle

The sum of the interior angles of a triangle is \(180^{\circ}\). Let \(\angle A=x\), \(\angle B = y\), \(\angle C=z\). So \(x + y+z=180^{\circ}\).

Step2: Analyze the property of an obtuse angle

Since \(\angle B\) is obtuse, \(y>90^{\circ}\). Then \(x + z=180^{\circ}-y\).

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

Because \(y > 90^{\circ}\), \(180^{\circ}-y<90^{\circ}\). And \(x + z=180^{\circ}-y\), so \(x<90^{\circ}\) (also \(z < 90^{\circ}\))

Answer:

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