Question

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

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 (right - angle).

Step3: Analyze Triangle B

Triangle B has an angle of \(110^{\circ}\gt90^{\circ}\).

Step4: Analyze Triangle C

All angles of Triangle C (\(35^{\circ},50^{\circ},95^{\circ}\)): \(35^{\circ}\lt90^{\circ}\), \(50^{\circ}\lt90^{\circ}\), \(95^{\circ}\lt90^{\circ}\)

Step5: Analyze Triangle D

All angles of Triangle D (\(80^{\circ},50^{\circ},50^{\circ}\)): \(80^{\circ}\lt90^{\circ}\), \(50^{\circ}\lt90^{\circ}\), \(50^{\circ}\lt90^{\circ}\)

Answer:

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