Final answer:
Carbon dating is the most accurate method for measuring the age of an Irish bog body with undecomposed organic matter.
Step-by-step explanation:
The most accurate way to measure the age of an Irish bog body that still has undecomposed organic matter is carbon dating.
Carbon dating is a chronometric dating method that relies on the decay of the radioactive isotope carbon-14 (¹4C) in once-living organisms. Once an organism dies, the amount of carbon-14 in its tissues begins to decay at a known rate, allowing scientists to determine the age of organic materials within a margin of error of 50 years.