Question

which angle number represents an angle vertical to ∠ehd?

Explanation:

Step1: Recall vertical angles definition

Vertical angles are opposite angles formed by two intersecting lines, they are equal in measure.

Step2: Identify lines forming ∠EHD

∠EHD is formed by lines EF and CD intersecting at H.

Step3: Find opposite angle to ∠EHD

The angle opposite to ∠EHD (which is ∠6) would be ∠4? Wait, no, wait. Wait, ∠EHD: let's label the angles. At point H, lines EF (with points E, H, F) and CD (with points C, G, H, D) intersect. So ∠EHD is angle 6? Wait, no, the angles at H: when two lines intersect, vertical angles are opposite. So ∠EHD (let's see the vertices: E - H - D, so the angle at H between EH and HD. Then the opposite angle would be between FH and HC? Wait, no, the lines are EF and CD. So the two intersecting lines are EF (E to F) and CD (C to D). So the angles at H: ∠4 (FH and CH), ∠5 (FH and DH), ∠6 (EH and DH), ∠EHF? Wait, no, the labels: angle 4 is between CH and FH, angle 5 between FH and DH, angle 6 between DH and EH, and the other angle (opposite to ∠6) would be angle 4? Wait, no, wait. Wait, vertical angles are formed when two lines cross. So line EF (E---H---F) and line CD (C---G---H---D) cross at H. So the four angles at H: ∠4 (between CH and FH), ∠5 (between FH and DH), ∠6 (between DH and EH), and ∠EHC? Wait, no, the angle opposite to ∠EHD (which is ∠6, since EH and DH form ∠6? Wait, maybe I mislabel. Wait, ∠EHD: vertex H, sides EH and DH. So the angle between EH (going to E) and DH (going to D) is ∠6. Then the vertical angle would be the angle opposite, which is between FH (going to F) and CH (going to C), which is ∠4? Wait, no, wait. Wait, when two lines intersect, vertical angles are non - adjacent and opposite. So line EF (E - H - F) and line CD (C - H - D) intersect at H. So the angles: ∠4 (F - H - C), ∠5 (F - H - D), ∠6 (D - H - E), ∠E - H - C. Wait, no, maybe the angle ∠EHD is ∠6 (D - H - E). Then the vertical angle would be ∠4 (C - H - F), because they are opposite each other when the two lines cross. Wait, no, let's think again. Vertical angles: if two lines intersect, say line 1 (A - B) and line 2 (C - D) intersect at O, then ∠AOC and ∠BOD are vertical angles, ∠AOD and ∠BOC are vertical angles. So in this case, lines EF (E - H - F) and CD (C - H - D) intersect at H. So ∠EHD: E - H - D, so the sides are EH and DH. The opposite angle would be F - H - C, which is ∠4? Wait, no, ∠EHD is angle 6 (assuming the labels: angle 4 is F - H - C, angle 5 is F - H - D, angle 6 is D - H - E, and angle E - H - C is... Wait, maybe the angle ∠EHD is angle 6, and its vertical angle is angle 4? Wait, no, maybe I got the labels wrong. Wait, the angle ∠EHD: vertex H, with E and D as the other points. So the angle between EH (towards E) and DH (towards D) is angle 6. Then the vertical angle is the angle between FH (towards F) and CH (towards C), which is angle 4? Wait, no, that doesn't seem right. Wait, maybe the angle ∠EHD is angle 6, and the vertical angle is angle 4? Wait, no, let's look at the intersection. When two lines intersect, vertical angles are equal and opposite. So line EF (E to F) and line CD (C to D) intersect at H. So the four angles: ∠4 (between CH and FH), ∠5 (between FH and DH), ∠6 (between DH and EH), and ∠EHC (between EH and CH). Wait, ∠EHD is ∠6 (DH and EH), so the vertical angle is ∠4 (CH and FH), because they are opposite. Wait, no, ∠EHC would be adjacent to ∠6. Wait, maybe I made a mistake. Wait, let's re - label: the two lines are EF (E - H - F) and CD (C - H - D). So the angles at H:
- ∠4: between CH (up to C) and FH (up to F)
- ∠5: between FH (up to F) and DH (down to D)
- ∠6: between DH (down to D) and EH (down to E)
- ∠EHC: between EH (down to E) and CH (up to C)

So ∠EHD is ∠6 (DH and EH). The vertical angle of ∠6 would be ∠4? No, ∠EHC is adjacent to ∠6. Wait, no, vertical angles are formed by the two intersecting lines. So line EF (E - F) and line CD (C - D) intersect at H. So the pairs of vertical angles are ∠4 and ∠6, and ∠5 and ∠EHC? Wait, no, ∠4 is between CH and FH, ∠6 is between DH and EH. Wait, maybe the angle ∠EHD is ∠6, and its vertical angle is ∠4. Because when you have two intersecting lines, the opposite angles are vertical. So if we consider line EF (E - H - F) and line CD (C - H - D), then ∠EHD (EH and DH) and ∠FHC (FH and CH) are vertical angles. And ∠FHC is angle 4. So the angle vertical to ∠EHD is angle 4? Wait, no, maybe I messed up the angle labels. Wait, the problem says "∠EHD", so vertex H, with E and D. So the angle is at H, between EH and DH. So the two lines forming this angle are EH (part of line EF) and DH (part of line CD). So the other two angles formed by the intersection of EF and CD at H are the angle between FH (part of EF) and CH (part of CD), which is angle 4. So ∠EHD (between EH and DH) and ∠FHC (between FH and CH) are vertical angles, and ∠FHC is angle 4. So the angle number is 4? Wait, no, maybe I got the angle labels wrong. Wait, looking at the diagram, angle 4 is between CH and FH, angle 5 between FH and DH, angle 6 between DH and EH, and angle 3? No, angle 3 is at G. Wait, at point G, we have angles 1,2,3. At point H, angles 4,5,6. So ∠EHD: E - H - D, so that's angle 6. Then the vertical angle would be angle 4, because they are opposite when lines EF and CD intersect. So the angle vertical to ∠EHD is angle 4? Wait, no, maybe I made a mistake. Wait, vertical angles are equal and opposite. So if ∠EHD is angle 6, then its vertical angle is angle 4? Wait, let's confirm the definition: vertical angles are two angles that are opposite each other when two lines cross. So when two lines intersect, they form two pairs of vertical angles. So in this case, lines EF and CD intersect at H. So the two pairs are ∠4 and ∠6, and ∠5 and the angle adjacent to ∠6 and ∠5 (let's say ∠EHC). Wait, ∠4 and ∠6: ∠4 is F - H - C, ∠6 is D - H - E. Are these opposite? Let's see the lines: EF is E - H - F, CD is C - H - D. So the intersection creates four angles: ∠F - H - C (4), ∠F - H - D (5), ∠D - H - E (6), ∠E - H - C (let's call it 7, but it's not labeled). Wait, maybe the angle ∠EHD is angle 6, and its vertical angle is angle 4, because they are opposite. So the answer should be 4? Wait, no, maybe I got the angle wrong. Wait, ∠EHD: E, H, D. So the angle is at H, with sides EH (going to E) and DH (going to D). So the vertical angle would be the angle at H with sides FH (going to F) and CH (going to C), which is angle 4. So the angle number is 4.

Answer:

4