Question

are the triangles below acute, obtuse, or right?
triangle a: angles 50°, 75°, 55°; options: acute (selected), obtuse, right
triangle b: angles 30°, 60°, right angle; options: acute, obtuse, right (selected)
triangle c: angles 110°, 40°, 30°; options: acute (selected), obtuse, right
triangle d: angles 50°, 50°, 80°; options: acute (selected), obtuse, right

Explanation:

Step1: Recall Triangle Types

• Acute: All angles < 90°.
• Right: One angle = 90°.
• Obtuse: One angle > 90°.

Step2: Analyze Triangle A

Angles: 50°, 75°, 55°. All < 90° → Acute. Correct.

Step3: Analyze Triangle B

Has a right angle (90°) → Right. Correct.

Step4: Analyze Triangle C

Angle 110° > 90° → Obtuse. But marked Acute (incorrect). Wait, recheck: 110° is obtuse. Wait, maybe typo? Wait, original: Triangle C angles 110°, 40°, 30°? Wait 110+40+30=180. 110>90 → Obtuse. But marked Acute? Wait, maybe user input error. But proceed.

Step5: Analyze Triangle D

Angles 50°, 50°, 80°? Wait 50+50+80=180. All <90 → Acute. Correct.

But for each:

Triangle A: All angles <90 → Acute. Correct.

Triangle B: Has 90° → Right. Correct.

Triangle C: 110° >90 → Obtuse. But marked Acute? Maybe mistake, but per analysis.

Triangle D: All <90 → Acute. Correct.

But the question is to determine each. Let's confirm each:

• Triangle A: 50,75,55. All acute → Acute. Correct.

• Triangle B: 30,60,90 (right angle) → Right. Correct.

• Triangle C: 110 (obtuse), 40, 30 → Obtuse. But marked Acute? Maybe error, but per angle sum.

• Triangle D: 50,50,80 (all <90) → Acute. Correct.

But the options given:

For Triangle A: Correct (Acute).

Triangle B: Correct (Right).

Triangle C: Should be Obtuse, but marked Acute? Maybe typo.

Triangle D: Correct (Acute).

But the task is to determine each. Let's go step by step.

Answer:

• Triangle A: Acute (all angles < 90°: 50°, 75°, 55°).
• Triangle B: Right (has a 90° angle).
• Triangle C: Obtuse (has a 110° angle > 90°).
• Triangle D: Acute (all angles < 90°: 50°, 50°, 80°).

(Note: If following the marked options, Triangle C’s marked “Acute” is incorrect; it should be Obtuse. Triangle D is correct as Acute.)