.
/_ACS=/_ABC=67^@∠ACS=∠ABC=67∘ because they both face arc ACAC and are half the measure of that arc.
/_BAC=90^@∠BAC=90∘ because it is an inscribed angle facing the diameter of the circle.
/_BCT=180^@-(90^@+67^@)=23^@∠BCT=180∘−(90∘+67∘)=23∘
/_ABC=/_BTC+/_BCT∠ABC=∠BTC+∠BCT because /_ABC∠ABC is the exterior angle of triangle DeltaBTC.
67^@=/_BTC+23^@
/_BTC=67^@-23^@=44^@