diff --git a/pandas/core/indexes/base.py b/pandas/core/indexes/base.py
index 623ce68201492..327c85e6c2d14 100644
--- a/pandas/core/indexes/base.py
+++ b/pandas/core/indexes/base.py
@@ -924,7 +924,9 @@ def format(
 
         return self._format_with_header(header, na_rep=na_rep)
 
-    def _format_with_header(self, header, na_rep="NaN") -> List[str_t]:
+    def _format_with_header(
+        self, header: List[str_t], na_rep: str_t = "NaN"
+    ) -> List[str_t]:
         from pandas.io.formats.format import format_array
 
         values = self._values
diff --git a/pandas/core/indexes/category.py b/pandas/core/indexes/category.py
index 4990e6a8e20e9..cbb30763797d1 100644
--- a/pandas/core/indexes/category.py
+++ b/pandas/core/indexes/category.py
@@ -347,7 +347,7 @@ def _format_attrs(self):
             attrs.append(("length", len(self)))
         return attrs
 
-    def _format_with_header(self, header, na_rep="NaN") -> List[str]:
+    def _format_with_header(self, header: List[str], na_rep: str = "NaN") -> List[str]:
         from pandas.io.formats.printing import pprint_thing
 
         result = [
diff --git a/pandas/core/indexes/datetimelike.py b/pandas/core/indexes/datetimelike.py
index 6d9d75a69e91d..c455e4831200e 100644
--- a/pandas/core/indexes/datetimelike.py
+++ b/pandas/core/indexes/datetimelike.py
@@ -362,7 +362,9 @@ def format(
 
         return self._format_with_header(header, na_rep=na_rep, date_format=date_format)
 
-    def _format_with_header(self, header, na_rep="NaT", date_format=None) -> List[str]:
+    def _format_with_header(
+        self, header: List[str], na_rep: str = "NaT", date_format: Optional[str] = None
+    ) -> List[str]:
         return header + list(
             self._format_native_types(na_rep=na_rep, date_format=date_format)
         )
diff --git a/pandas/core/indexes/interval.py b/pandas/core/indexes/interval.py
index e8d0a44324cc5..9281f8017761d 100644
--- a/pandas/core/indexes/interval.py
+++ b/pandas/core/indexes/interval.py
@@ -948,7 +948,7 @@ def take(self, indices, axis=0, allow_fill=True, fill_value=None, **kwargs):
     # Rendering Methods
     # __repr__ associated methods are based on MultiIndex
 
-    def _format_with_header(self, header, na_rep="NaN") -> List[str]:
+    def _format_with_header(self, header: List[str], na_rep: str = "NaN") -> List[str]:
         return header + list(self._format_native_types(na_rep=na_rep))
 
     def _format_native_types(self, na_rep="NaN", quoting=None, **kwargs):