If each of alpha beta and gamma is a positive acute angle such that sin alpha + beta minus gama equals to half coma cos beta + gamma minus alpha equals to half and tan gamma + alpha minus beta equals to one find the values of alpha beta and gamma

α + β - γ = 30 (i)

β + γ - α = 60 (ii)

γ + α - β = 45 (iii)

Adding (i) and (ii)
2 beta = 90 degree
beta = 45 degree

Adding (ii) and (iii)
2 gamma = 105 degree
gamma = 52.5 degree

Putting values of beta and gamma in (i) we get 
alpha + 45 degree - 52.5 degree = 30 degree
alpha = 30 + 7.5
= 37.5 degree