In a Dockerfile, How to update PATH environment variable?

I have a dockerfile that download and builds GTK from source, but the following line is not updating my image's environment variable:

RUN PATH="/opt/gtk/bin:$PATH"
RUN export PATH

I read that that I should be using ENV to set environment values, but the following instruction doesn't seem to work either:

ENV PATH /opt/gtk/bin:$PATH

This is my entire Dockerfile:

FROM ubuntu
RUN apt-get update
RUN apt-get install -y golang gcc make wget git libxml2-utils libwebkit2gtk-3.0-dev libcairo2 libcairo2-dev libcairo-gobject2 shared-mime-info libgdk-pixbuf2.0-* libglib2-* libatk1.0-* libpango1.0-* xserver-xorg xvfb

# Downloading GTKcd
RUN wget http://ftp.gnome.org/pub/gnome/sources/gtk+/3.12/gtk+-3.12.2.tar.xz
RUN tar xf gtk+-3.12.2.tar.xz
RUN cd gtk+-3.12.2

# Setting environment variables before running configure
RUN CPPFLAGS="-I/opt/gtk/include"
RUN LDFLAGS="-L/opt/gtk/lib"
RUN PKG_CONFIG_PATH="/opt/gtk/lib/pkgconfig"
RUN export CPPFLAGS LDFLAGS PKG_CONFIG_PATH
RUN ./configure --prefix=/opt/gtk
RUN make
RUN make install

# running ldconfig after make install so that the newly installed libraries are found.
RUN ldconfig

# Setting the LD_LIBRARY_PATH environment variable so the systems dynamic linker can find the newly installed libraries.
RUN LD_LIBRARY_PATH="/opt/gtk/lib"

# Updating PATH environment program so that utility binaries installed by the various libraries will be found.
RUN PATH="/opt/gtk/bin:$PATH"
RUN export LD_LIBRARY_PATH PATH

# Collecting garbage
RUN rm -rf gtk+-3.12.2.tar.xz

# creating go code root
RUN mkdir gocode
RUN mkdir gocode/src
RUN mkdir gocode/bin
RUN mkdir gocode/pkg

# Setting the GOROOT and GOPATH enviornment variables, any commands created are automatically added to PATH
RUN GOROOT=/usr/lib/go
RUN GOPATH=/root/gocode
RUN PATH=$GOPATH/bin:$PATH
RUN export GOROOT GOPATH PATH

You can use Environment Replacement in your Dockerfile as follows:

ENV PATH="/opt/gtk/bin:${PATH}"

Although the answer that Gunter posted was correct, it is not different than what I already had posted. The problem was not the ENV directive, but the subsequent instruction RUN export $PATH

There's no need to export the environment variables, once you have declared them via ENV in your Dockerfile.

As soon as the RUN export ... lines were removed, my image was built successfully