Question

use the diagram to classify each angle as acute, right, obtuse, or straight. drag & drop the answer ∠cge ∠bgf ∠bga ∠ega acute right obtuse straight

Explanation:

To solve this, we analyze each angle using the definitions:

• Acute Angle: Less than \( 90^\circ \).
• Right Angle: Exactly \( 90^\circ \).
• Obtuse Angle: Greater than \( 90^\circ \) but less than \( 180^\circ \).
• Straight Angle: Exactly \( 180^\circ \).

1. \( \angle CGE \)

From the diagram, \( \angle CGE \) is marked with a right - angle symbol, so it measures \( 90^\circ \). Thus, \( \angle CGE \) is a right angle.

2. \( \angle BGF \)

Visually, \( \angle BGF \) is smaller than \( 90^\circ \) (since it is narrower than the right angle \( \angle CGE \)). So, \( \angle BGF \) is an acute angle.

3. \( \angle BGA \)

\( \angle BGA \) is wider than \( 90^\circ \) (broader than the right angle \( \angle CGE \)) but less than \( 180^\circ \). So, \( \angle BGA \) is an obtuse angle.

4. \( \angle EGA \)

\( \angle EGA \) forms a straight line (since points \( E \), \( G \), and \( A \) are colinear), so it measures \( 180^\circ \). Thus, \( \angle EGA \) is a straight angle.

Final Categorization:

• Acute: \( \angle BGF \)
• Right: \( \angle CGE \)
• Obtuse: \( \angle BGA \)
• Straight: \( \angle EGA \)

To complete the drag - and - drop:

• Drag \( \angle CGE \) to “Right”.
• Drag \( \angle BGF \) to “Acute”.
• Drag \( \angle BGA \) to “Obtuse”.
• Drag \( \angle EGA \) to “Straight”.

Answer:

To solve this, we analyze each angle using the definitions:

• Acute Angle: Less than \( 90^\circ \).
• Right Angle: Exactly \( 90^\circ \).
• Obtuse Angle: Greater than \( 90^\circ \) but less than \( 180^\circ \).
• Straight Angle: Exactly \( 180^\circ \).

1. \( \angle CGE \)

From the diagram, \( \angle CGE \) is marked with a right - angle symbol, so it measures \( 90^\circ \). Thus, \( \angle CGE \) is a right angle.

2. \( \angle BGF \)

Visually, \( \angle BGF \) is smaller than \( 90^\circ \) (since it is narrower than the right angle \( \angle CGE \)). So, \( \angle BGF \) is an acute angle.

3. \( \angle BGA \)

\( \angle BGA \) is wider than \( 90^\circ \) (broader than the right angle \( \angle CGE \)) but less than \( 180^\circ \). So, \( \angle BGA \) is an obtuse angle.

4. \( \angle EGA \)

\( \angle EGA \) forms a straight line (since points \( E \), \( G \), and \( A \) are colinear), so it measures \( 180^\circ \). Thus, \( \angle EGA \) is a straight angle.

Final Categorization:

• Acute: \( \angle BGF \)
• Right: \( \angle CGE \)
• Obtuse: \( \angle BGA \)
• Straight: \( \angle EGA \)

To complete the drag - and - drop:

• Drag \( \angle CGE \) to “Right”.
• Drag \( \angle BGF \) to “Acute”.
• Drag \( \angle BGA \) to “Obtuse”.
• Drag \( \angle EGA \) to “Straight”.