4)
MO=2y+1
LN=8y-10
in a rectangle all diagonals are congruent (=have the same length)
so 2*MO=LN
2*(2y+1)=8y-10
4y+2=8y-10
12=4y
3=y
insert y=3 into LN:
8y-10=
8*3-10=
24-10=14=LN
5)
m<OML=30°
m<OLM=m<OML=30° (the triangle formed by the diagonals to the center has equal angles in the rectangle's corners)
a triangle has an internal angle sum of 180°
so m<LOM=180-30-30=120°
6)
m<MON=48° (center angle)
m<OMN=2z+6 (one of the cornes)
a triangle has an internal angle sum of 180°
if we subtract the center angle we receive the sum of both corner angles
-> 180-m<MON=180-48=132°=2*corner angles
again both corner angles are equal-> divide by 2 to get a single one
132/2=66=m<OMN=m<ONM
m<OMN=66=2z+6
60=2z
30=z
