Question

in words, type what kind of angle is formed.

• ∠bgc forms an angle.
• ↔ae forms a angle.
• ∠dga forms a angle.
• ∠egf forms a angle.

Answer:

To solve this, we analyze each angle based on their measures (acute < 90°, right = 90°, obtuse > 90° < 180°, straight = 180°):

For ∠BGC:

The angle between BG and GC is less than 90°, so it's an acute angle.

For $\overleftrightarrow{AE}$:

Line AE is vertical, and when combined with the horizontal line (like FC), it forms a 180° angle? Wait, no—$\overleftrightarrow{AE}$ is a straight line (since A - G - E are colinear), so it forms a straight angle (180°). Wait, or maybe the angle formed by AE with another line? Wait, the diagram shows AE as a vertical line, and FC as horizontal, intersecting at G with right angles (the pink squares indicate right angles, 90°). Wait, maybe the question is about the angle formed by $\overleftrightarrow{AE}$ with, say, FC? But the pink squares at G (between AE and FC) show right angles. Wait, re-reading: " $\overleftrightarrow{AE}$ forms a [ ] angle." Wait, a straight line (like $\overleftrightarrow{AE}$) is a straight angle (180°), but maybe the angle between AE and FC? Wait, the pink squares at G (between AE and FC) are right angles (90°). Wait, maybe the problem has a typo, but assuming:

• $\overleftrightarrow{AE}$ and $\overleftrightarrow{FC}$ intersect at G with right angles (the pink squares), so the angle between them is right? Wait, no—$\overleftrightarrow{AE}$ is a straight line (180°), but if the question is about the angle formed by AE with another line (like FC), then since AE ⊥ FC (pink squares), the angle is right (90°). Wait, maybe the intended question is the angle between AE and FC, which is right.

For ∠DGA:

Angle DGA: Let's see, BG and DG—wait, AE is vertical, GC is horizontal, BG is between AE and GC, DG is between GC and AE (below). So ∠DGA: from D to G to A. Let's visualize: A is up, D is down-right, G is center. So the angle between DG and AG: since AE is vertical, and DG is below GC (horizontal), the angle from DG to AG would be more than 90° (obtuse) or? Wait, AE (vertical) and FC (horizontal) are perpendicular (right angle). BG is in the first quadrant (A-G-C), DG is in the fourth quadrant (C-G-E? Wait, E is down, C is right, so D is between C and E. So ∠DGA: points D, G, A. So from D (down-right) to G to A (up). The angle here: since AE is vertical, and DG is at an angle, the angle between DG and AG—let's see, the right angle is between AE and FC (90°). ∠BGC is acute (less than 90°), ∠DGA: let's see, if ∠BGC is acute, then ∠DGA would be obtuse (since it's more than 90° but less than 180°).

For ∠EGF:

Points E, G, F. E is down, G is center, F is left. So ∠EGF: from E to G to F. Since E-G is vertical down, F-G is horizontal left, so the angle between them is 90° (right angle, as indicated by the pink square at G between E and F? Wait, the pink squares: one between A-G-F? No, the diagram has two pink squares: one between A-G-C? Wait, the original diagram: "pink square" at G, maybe between AE and FC (vertical and horizontal), so ∠EGF: E (down), G, F (left)—so vertical down and horizontal left, forming a right angle (90°).

Final Answers:

• ∠BGC: acute
• $\overleftrightarrow{AE}$ (assuming angle with FC): right (or straight, but likely right due to the pink square)
• ∠DGA: obtuse
• ∠EGF: right

(Note: The exact labels depend on the diagram’s precision, but based on typical angle types:

• Acute: <90°, Right: =90°, Obtuse: >90°<180°, Straight: =180°.)

So filling in:

• ∠BGC: acute
• $\overleftrightarrow{AE}$: straight (if it’s a straight line) or right (if angle with FC). Assuming the problem means the angle formed by $\overleftrightarrow{AE}$ with $\overleftrightarrow{FC}$, it’s right.
• ∠DGA: obtuse
• ∠EGF: right

(Adjusted based on standard angle definitions:

• ∠BGC: acute (small angle between BG and GC)
• $\overleftrightarrow{AE}$: straight (since it’s a straight line, 180°)
• ∠DGA: obtuse (angle greater than 90°)
• ∠EGF: right (angle between vertical down and horizontal left, 90°)

Final answers (filling the blanks):

• ∠BGC: acute
• $\overleftrightarrow{AE}$: straight
• ∠DGA: obtuse
• ∠EGF: right