Question

are the triangles below acute, obtuse, or right?
triangle a
triangle b
triangle c
triangle d
acute
obtuse
right
acute
obtuse
right
acute
obtuse
right
acute
obtuse
right

Explanation:

Step1: Recall triangle - type definitions

• Acute triangle: All angles \(<90^{\circ}\)
• Right triangle: One angle \( = 90^{\circ}\)
• Obtuse triangle: One angle \(>90^{\circ}\)

Step2: Analyze Triangle A

All angles \(50^{\circ},50^{\circ},80^{\circ}\) (since \(180-(50 + 50)=80\)). All \(<90^{\circ}\), so acute.

Step3: Analyze Triangle B

One angle \( = 90^{\circ}\), so right.

Step4: Analyze Triangle C

One angle \(110^{\circ}>90^{\circ}\), so obtuse.

Step5: Analyze Triangle D

All angles \(50^{\circ},55^{\circ},75^{\circ}\) (since \(180-(50 + 55)=75\)). All \(<90^{\circ}\), so acute.

Answer:

Triangle A: Acute; Triangle B: Right; Triangle C: Obtuse; Triangle D: Acute