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.
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.