Triangle ABC is an obtuse triangle with an obtuse angle at vertex B. Then angle a must be ___.

Question: Triangle ABC is an obtuse triangle with an obtuse angle at vertex B. Then angle a must be ___.

A triangle is a closed figure or shape with 3 sides, 3 angles, and 3 vertices.

Answer: If ΔABC is an obtuse triangle with an obtuse angle at vertex B, then ∠A must be an acute angle.

Let us explore more about the angles of the triangle.

Explanation:

The sum of the angles of a triangle adds up to 180°

∠A + ∠B + ∠C = 180°

If ∠B is an obtuse angle, ∠B > 90°

∠A + ∠C < 180° - 90°

∠A + ∠C < 90°

∠A, ∠C both less than 90°

∠A, ∠C must be acute angles.

Thus, if ΔABC is an obtuse triangle with an obtuse angle at vertex B, then ∠A must be an acute angle.