diff --git a/typeface.py b/typeface.py
index 5904889..74a8f93 100644
--- a/typeface.py
+++ b/typeface.py
@@ -487,7 +487,7 @@ def draw_letter_v(unit):
     left(45)
     pendown()
     forward(unit * sqrt(2))
-    right(45)
+    left(45)
     forward(unit * 3)
     right(45)
     forward(unit * sqrt(2))
@@ -497,6 +497,19 @@ def draw_letter_v(unit):
     penup()
     forward(unit * 4)
     left(90)
+    pendown()
+    forward(unit * 3)
+    left(45)
+    forward(unit * sqrt(2))
+    right(45)
+    forward(unit * 3)
+    left(45)
+    forward(unit * sqrt(2))
+    right(135)
+    penup()
+    forward(unit * 4)
+    right(180)
+
 
 def draw_letter_w(unit):
     penup()
@@ -524,7 +537,29 @@ def draw_letter_w(unit):
     left(180)
 
 def draw_letter_x(unit):
-    pass
+    penup()
+    forward(unit * 2)
+    left(90)
+    pendown()
+    forward(unit * 2)
+    right(45)
+    forward(unit * 4 * sqrt(2))
+    left(45)
+    forward(unit * 2)
+    left(90)
+    penup()
+    forward(unit * 4)
+    left(90)
+    pendown()
+    forward(unit * 2)
+    left(45)
+    forward(unit * 4 * sqrt(2))
+    right(45)
+    forward(unit * 2)
+    right(90)
+    penup()
+    forward(unit * 6)
+    right(180)
 
 def draw_letter_y(unit):
     penup()