Question

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

Explanation:

Step1: Recall triangle - type definitions

• A right - triangle has one angle equal to \(90^{\circ}\).
• An obtuse - triangle has one angle greater than \(90^{\circ}\).
• An acute - triangle has all angles less than \(90^{\circ}\).

Step2: Analyze Triangle A

Triangle A has a \(90^{\circ}\) angle. So, by the definition of a right - triangle, it is a right - triangle.

Step3: Analyze Triangle B

Triangle B has an angle of \(130^{\circ}\gt90^{\circ}\). So, by the definition of an obtuse - triangle, it is an obtuse - triangle.

Step4: Analyze Triangle C

Triangle C has an angle of \(115^{\circ}\gt90^{\circ}\). So, by the definition of an obtuse - triangle, it is an obtuse - triangle.

Step5: Analyze Triangle D

For Triangle D, check the angles: \(55^{\circ}\lt90^{\circ}\), \(50^{\circ}\lt90^{\circ}\), \(75^{\circ}\lt90^{\circ}\). Since all angles are less than \(90^{\circ}\), by the definition of an acute - triangle, it is an acute - triangle.

Answer:

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