If the div announcementimmediately follows the div content, use:
<xsl:template match="div[@id='content' and following-sibling::div[1][@id='announcement']">
<xsl:copy>
<xsl:copy-of select="@*" />
<xsl:copy-of select="following-sibling::div[1][@id='announcement']" />
<xsl:apply-templates />
</xsl:copy>
</xsl:template>
<xsl:template match="div[@id='announcement' and preceding-sibling::div[1][@id='content']" />
The above is enough to not touch on any other sections that may be in your document. If your situation allows, you can make it simpler / less specific to increase readability.