Question

are the triangles below acute, obtuse, or right?
triangle a: angles 30°, 30°, 120°
triangle b: angles 45°, 45°, right angle
triangle c: angles 55°, 50°, 75°
triangle d: angles 50°, 80°, 50°
options for each triangle: acute, obtuse, right

Explanation:

Step1: Analyze Triangle A

A triangle is obtuse if it has one angle greater than \(90^\circ\). Triangle A has a \(120^\circ\) angle, so it's obtuse.

Step2: Analyze Triangle B

A right triangle has one \(90^\circ\) angle. Triangle B has a right angle (the square corner), so it's right.

Step3: Analyze Triangle C

An acute triangle has all angles less than \(90^\circ\). Triangle C's angles are \(55^\circ\), \(50^\circ\), \(75^\circ\) (all \(< 90^\circ\)), so it's acute.

Step4: Analyze Triangle D

All angles in Triangle D (\(50^\circ\), \(50^\circ\), \(80^\circ\)) are less than \(90^\circ\), so it's acute.

Answer:

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