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

Step2: Analyze Triangle A

Triangle A has an angle of \(90^{\circ}\). By the definition of a right - triangle (a triangle with one \(90^{\circ}\) angle), it is a right triangle.

Step3: Analyze Triangle B

Triangle B has an angle of \(110^{\circ}>90^{\circ}\). By the definition of an obtuse triangle (a triangle with one angle greater than \(90^{\circ}\)), it is an obtuse triangle.

Step4: Analyze Triangle C

Triangle C has an angle of \(115^{\circ}>90^{\circ}\). By the definition of an obtuse triangle (a triangle with one angle greater than \(90^{\circ}\)), it is an obtuse triangle.

Step5: Analyze Triangle D

For Triangle D, the angles are \(50^{\circ},50^{\circ},80^{\circ}\). Since \(50^{\circ}<90^{\circ}\) and \(80^{\circ}<90^{\circ}\), all angles are less than \(90^{\circ}\). By the definition of an acute triangle (a triangle with all angles less than \(90^{\circ}\)), it is an acute triangle.

Answer:

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