Question

Please explain how and give the answer!

Answer 1

Opposite angles of a rhombus are congruent 
so
m<A = m<C
m<B = m<D
24(10-x)=6(x+15)
240 - 24x = 6x+90
30x = 150
x = 5

24(10-x) = 24(10-5) = 24(5) = 120
so m<B=m<D = 120

rhombus sum of interior = 360

360 - 120 -120 = 120

m<A = m<C = 120/2 = 60

answer

m<C = 60

Answer 2

The mass of b equals the mass of d so
24(10-x)=6(x+15)
240-24x=6x+90
30x=150
x=5
mass of d is 6(5+15)=6*20=120
mass of c=180-mas of d=180-120=60°