Question

The secretary apologized to the prime minister ________ late to the meeting.

Answer 1

The correct words to be filled in the given blank are as shown below:

The secretary apologized to the prime minister for being late to the meeting.

'For' is used to show a reason or cause.  

Answer 2

Here is your answer 
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The secretary apologized to the prime minister for being late to the meeting.

______________________________

for is used as cause and reasons