Preheat the oven to 350 degrees F. Move a rack to the bottom position.
Drain the mandarin oranges and reserve the liquid. Measure the reserved liquid and add enough water to equal 1 1/4 cups. Measure out 1 cup mandarin oranges, reserving the remaining oranges for garnish.
In a large mixing bowl, combine angel food cake mix, mandarin water, orange extract and orange zest. With an electric mixer, beat on low speed for 30 seconds. Scrape down sides of bowl and beat on medium for 1 minute. Pour into angel food tube pan. Carefully place 1 cup of orange segments around top of cake batter. Bake for 35 to 45 minutes, or until top of cake is cracked, dark golden brown, and not sticky.
Remove cake from oven and invert onto glass bottle to cool.
Frost cake with whipped topping and garnish with reserved orange segments.
Cook's Note: Excessive stirring will cause whipped topping to become watery.