(으)려던 참이다 is used at the end of a sentence to show that you were about to do something:
너한테 전화를 하려던 참이었어요.
I was just about to call you.
지금 나가려던 참이었어요.
I was about to leave now.
– 박물관에 같이 갈까요?
– Shall we go to the museum together?
– 안 그래도, 가려던 참이었어요. 같이 갈래요.
– Actually, I was just about to go. Let’s go together.
– 지금 뭐 해요?
– What are you doing now?
– 얼굴을 세수하고 잠을 자려던 참이었어요.
– I was about to wash my face and go to sleep.
– 지금은 바빠요?
– Are you busy right now?
– 안 그래도, 밥을 먹으려던 참이었어요. 15분 후에 돌아오세요.
– Actually, I was about to eat a meal. Come back in 15 minutes.