Question

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

Explanation:

Step1: Analyze Triangle A

A triangle is acute if all angles are less than \(90^{\circ}\). In Triangle A, the angles are \(60^{\circ}\), \(50^{\circ}\), and \(70^{\circ}\) (since \(180-(60 + 50)=70\)). All are less than \(90^{\circ}\).

Step2: Analyze Triangle B

A triangle is obtuse if one angle is greater than \(90^{\circ}\). In Triangle B, one angle is \(110^{\circ}>90^{\circ}\).

Step3: Analyze Triangle C

A triangle is acute if all angles are less than \(90^{\circ}\). In Triangle C, the angles are \(75^{\circ}\), \(50^{\circ}\), and \(55^{\circ}\) (since \(180-(75 + 50)=55\)). All are less than \(90^{\circ}\).

Step4: Analyze Triangle D

A triangle is right - angled if one angle is \(90^{\circ}\). In Triangle D, one angle is \(90^{\circ}\).

Answer:

Triangle A: Acute; Triangle B: Obtuse; Triangle C: Acute; Triangle D: Right - angled.