Standardize the #includes in runtime/include/*h.

Bug: https://github.com/dart-lang/sdk/issues/35172
Change-Id: I75d1e99fb178d7b6df051f6ada0a26a126e31b81
Reviewed-on: https://dart-review.googlesource.com/c/84542
Commit-Queue: Liam Appelbe <liama@google.com>
Reviewed-by: Siva Annamalai <asiva@google.com>
diff --git a/runtime/BUILD.gn b/runtime/BUILD.gn
index ecf8a5d..adbfaa6 100644
--- a/runtime/BUILD.gn
+++ b/runtime/BUILD.gn
@@ -133,7 +133,7 @@
     defines += [ "NDEBUG" ]
   }
 
-  include_dirs = []
+  include_dirs = [ "include" ]
   if (dart_use_tcmalloc) {
     defines += [ "DART_USE_TCMALLOC" ]
     include_dirs += [ "../third_party/tcmalloc/gperftools/src" ]
diff --git a/runtime/include/bin/dart_io_api.h b/runtime/include/bin/dart_io_api.h
index 07a384c..e194f7a 100644
--- a/runtime/include/bin/dart_io_api.h
+++ b/runtime/include/bin/dart_io_api.h
@@ -5,7 +5,7 @@
 #ifndef RUNTIME_INCLUDE_BIN_DART_IO_API_H_
 #define RUNTIME_INCLUDE_BIN_DART_IO_API_H_
 
-#include "include/dart_tools_api.h"
+#include "dart_tools_api.h"
 
 namespace dart {
 namespace bin {
diff --git a/runtime/include/dart_tools_api.h b/runtime/include/dart_tools_api.h
index 5452c25..809177b 100644
--- a/runtime/include/dart_tools_api.h
+++ b/runtime/include/dart_tools_api.h
@@ -5,7 +5,7 @@
 #ifndef RUNTIME_INCLUDE_DART_TOOLS_API_H_
 #define RUNTIME_INCLUDE_DART_TOOLS_API_H_
 
-#include "include/dart_api.h"
+#include "dart_api.h"
 
 /** \mainpage Dart Tools Embedding API Reference
  *