Triangle Properties and Angle Relationships

What is the fundamental definition of a triangle?

• A polygon with 4 sides, 4 angles, and 4 vertices.

• A closed polygon with 3 sides, 3 angles, and 3 vertices.

• An open shape with 3 sides and 3 angles.

• A polygon with 3 sides and 2 vertices.

Which of the following correctly identifies the primary components of a triangle?

• Sides, edges, and faces

• Lines, curves, and points

• Sides, vertices, and angles

• Base, height, and hypotenuse

What is the sum of the three interior angles of any triangle?

• 90 degrees

• 180 degrees

• 270 degrees

• 360 degrees

A right-angled triangle has two known angles: 90 degrees and 24 degrees. What is the measure of the third angle?

• 56 degrees

• 66 degrees

• 76 degrees

• 86 degrees

Can a triangle be constructed with angle measures of 33°, 44°, and 93°?

• Yes, because the sum is 180°.

• No, because the sum is less than 180°.

• Yes, because all angles are acute.

• No, because the sum is greater than 180°.

Can a triangle be constructed with angle measures 33°, 44°, and 93°?

• Yes, because the sum is 180°

• No, because the sum is not 180°

• Yes, because all angles are acute

• No, because one angle is obtuse

The angles of a triangle are in the ratio 1:2:6. What are the measures of the angles?

• 10°, 20°, 60°

• 20°, 40°, 120°

• 30°, 60°, 90°

• 15°, 30°, 90°

What is the relationship between an exterior angle of a triangle and its two remote interior angles?

• The exterior angle is half the sum of the remote interior angles.

• The exterior angle is equal to the sum of the remote interior angles.

• The exterior angle is equal to the difference of the remote interior angles.

• The exterior angle is equal to the product of the remote interior angles.

A triangle has two interior angles measuring 63° and 84°. What is the measure of the exterior angle adjacent to the third interior angle?

• 147°

• 180°

• 100°

• 120°