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How do you solve problems like this? I solved one earlier just like this except sans friction and I used (and it worked)

a = (m1g sin(alpha) - m2g sin (beta))/(m1+m2)

so for this one I tried a = ((m1g sin(alpha) - m1(mu)g cos(alpha)) - (m2g sin (beta) - m2(mu)g cos(beta))/(m1+m2)

I think the problem is that I didn't include the tension of the other block when finding a blocks normal force, but I'm not sure how to go about finding this.

Also, In our text, for a mass hanging straight down held by a string, it gives the equation Tension - mg = -ma

does this just mean that the force of tension minus the force of gravity equals the total acceleration of the mass?

Much thanks to anyone who contributes some advice or direction.

the diagram