A Board of Appeals shall be appointed by the Board of Trustees, pursuant to the Village Law.

In addition to the powers granted to the Board of Trustees under Article 7 of the Village Law and § 271-130 of this chapter relating to the establishment of a Board of Appeals, which provisions are incorporated herein by reference, the Board of Trustees is hereby empowered to appoint up to four ad hoc members to the Board of Appeals when, due to disqualification, absenteeism, unavailability, conflict of interest or any other reason, a quorum of members is not present to conduct the business of the Board of Appeals. No more than two such ad hoc members may attend and serve at the same meeting of the Board of Appeals. In all other respects, the powers of the Board of Trustees as provided in Article 7 of the Village Law are not diminished, enlarged or revoked by this subsection.

Vary the application of the regulations herein established and establish appropriate requirements for irregular lots or lots less than the required area in any district existing at the effective date of this chapter.

Vary the application of the regulations herein established and modify the requirements hereof in cases of exceptional topography under such conditions as will safeguard the neighborhood.

Grant temporary and conditional permits of limited duration for nonconforming uses and buildings in undeveloped sections.

Determine and establish the true location of district boundaries in any disputed case.

Where a zone boundary line divides a lot in a single ownership at the effective date of this chapter, permit a use authorized on either portion of such lot to extend to the entire lot, but not more than 25 feet beyond the boundary line of the greater restricted zone.

Permit the extension of a nonconforming use of a building upon the lot occupied by such use of a building at the effective date of this chapter.

Vary side and rear yard restrictions in Residence R-4 Districts, as provided in Article VII, § 271-65, hereof.

Vary side yard restrictions for buildings other than dwellings in Residence R, Residence R-1, Residence R-2, Residence R-3 and Residence R-4 Districts.

Vary the height regulations in any district to permit church spires, belfries, towers designed exclusively for ornamental purposes, flag staffs, chimneys, flues or scenery lofts and parapet walls extending not more than three feet above the height permitted by these regulations.

Vary the application of the regulations herein established, and establish appropriate requirements for the location, number and size of signs in any district.

When, in its judgment, the public convenience and welfare will be substantially served and the appropriate use of neighboring property will not be substantially or permanently injured, the Board of Appeals may, in a special case after public notice and hearing and subject to appropriate conditions and safeguards, and provided that the same is in harmony with the general purpose of this chapter, authorize as a special exception churches, parochial schools, private schools and clubs not operated for profit. Before the authorization of such uses, the owner shall file a verified petition with the Board of Appeals, which petition shall set forth such facts as shall be required by the Board of Appeals and shall also be accompanied by plans of all buildings and structures intended to be erected upon the premises and plans showing the location of the intended buildings and structures upon the property affected and such other details as the Board of Appeals may require. The Board of Appeals shall require that the applicant provide an off-street parking area of such size as in the judgment of the Board of Appeals shall be adequate for the number of persons who may be accommodated in such building and structures and as shall promote the health, safety and welfare of the inhabitants of the Village.

When, in its judgment, the public convenience and welfare will be substantially served and the appropriate use of neighboring property will not be substantially or permanently impaired, the Board of Appeals may, in a special case after public notice and hearing and subject to appropriate conditions and safeguards, and provided that the same is in harmony with the general purpose of this chapter, authorize as a special exception in a Business B District automobile service stations or public garages. Before such use is authorized, the owner shall file a verified petition with the Board of Appeals, which petition shall set forth such facts as shall be required by the Board of Appeals. Accompanying said petition shall be the survey of the plot showing the location of all proposed structures, tanks, signs and such other details as shall be required by the Board of Appeals and shall also be accompanied by the written consent of 80% in number of the owners and mortgagees of all property within 200 feet of any portion of the lot or plot on which the automobile service station is to be erected; such consent shall not be limited to property owners within the Village but shall include all property owners, whether within or without the Village. A fee of $100 shall accompany said application and be paid to the Village Clerk. No application shall be accepted, nor shall any action be taken by the Board of Appeals, unless it shall comply with the provisions of the conditions precedent. This section shall not apply to a Business A District planned business community or any other planned business zoning area hereafter created by ordinance.

The erection or enlargement of a public garage or automobile service station or the conversion of any premises not so used to be used for such purposes, if otherwise allowed, shall not be permitted if any point or part of the lot or plot is situated at a distance of 200 feet from any point of a lot or plot upon which any of the following enumerated buildings are located. The buildings above referred to are:

When in its judgment the public convenience and welfare will be substantially served and the appropriate use of neighboring property will not be substantially or permanently injured, the Board of Appeals may, in a special case after public notice and hearing and subject to appropriate conditions and safeguards, and provided that the same is in harmony with the general purpose of this chapter, authorize as a special exception the installation and maintenance of a dish antenna. Before such accessory structure is authorized, the owner shall have filed a verified petition with the Board of Appeals, which petition shall set forth such facts as shall be required by the Board of Appeals and as set forth in Article XIX of this chapter.