Question

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Answer 1

ΔABD is an obtuse triangle

Explanation:

The type of a triangle according to its angle measures

1. The acute triangle ⇒ it has 3 acute angles
2. The right triangle ⇒ it has 1 right angle and 2 acute angles
3. The obtuse triangle ⇒ it has 1 obtuse angle and 2 acute angles

• 0° < acute angle < 90°

• right angle = 90°

• 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