Answer:
ΔABD is an obtuse triangle
Step-by-step explanation:
The type of a triangle according to its angle measures
- The acute triangle ⇒ it has 3 acute angles
- The right triangle ⇒ it has 1 right angle and 2 acute angles
- The obtuse triangle ⇒ it has 1 obtuse angle and 2 acute angles
- 90° < obtuse angle < 180°
In triangle ABD
∵ m∠ABD = 100°
∵ m∠BAD = 50°
→ The sum of the interior angles of a triangle is 180°
∴ m∠ABD + m∠BAD + m∠BDA = 180°
∴ 100 + 50 + m∠BDA = 180
∴ 150 + m∠BDA = 180
→ Subtract 150 from both sides
∴ m∠BDA = 30°
∵ m∠ABD = 100°
∴ ∠ABD is an obtuse angle
∵ m∠BAD = 50° and m∠BDA = 30°
∴ ∠BAD and ∠BDA are acute angles
∵ ΔABD has 1 obtuse angle and 2 acute angles
∴ ΔABD is an obtuse triangle
