In 1942, he earned a scholarship to study at Mfantsipim School, Cape Coast, for his secondary education.
[3][4][5] He later founded a law firm together with his friend, Kwabena Adu-Tutu Amankwah at Adum in Kumasi.
[3] Following recommendations from the presiding judge of the Ashanti Region and the Ghana Judicial Council, Agyapong was made a justice of the High Court in 1977.
[3] In 1980, he made history by being the only High Court judge to sit on the then transitional Supreme Court bench in the hearing of the historical constitutional case between the then People's National Party (PNP) government and Dr. Kwame Amoako Tuffuor.
[3][4] In May 1979, he was appointed chairman of the Committee of Enquiry that investigated the case of the Accra Railway shooting incident that saw the death of a second-year student of Commonwealth Hall, University of Ghana by a police constable.
In his report in June 1980, he lamented the unwarranted use of ammunition by the police in a rather peaceful students' demonstration.
Agyapong, like his three compatriots, had their lives and careers abruptly ended by their untimely deaths on June 30, 1982.