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The order glad I am is used after how. Other adjectives also follow the same pattern as glad.
How glad I am that you were able to attend our party!
I can't tell you how sorry I am about the death of your grandfather.
My smile reveals how happy I am about the test results.
Instead of I am you can also have you are, you were, he is, he was, and so on.
I was surprised how happy you were when you heard the news.
You can't imagine how tired she was after the race.
I had forgotten how tall they were.
CJ