Problem 8
Maxwell Lim
<ABC is bisected by ray BD. M<ABD=5x-4. M<DBC=3x+2. Find x and m<ABC
In order to begin to solve the equation you have to set up the equation for x.
m<ABD=5x-4 m<DBC=3x+2 Given
m<ABD+m<DBC=m<ABC Angle Addition Postulate
m<ABD=m<DBC Definition of Angle Bisection
5x+-4=3x+2 Substitution Property
2x-4=2 Subtraction Property
2x=6 Addition Property
x=3 Division Property
Now that we have found x the next thing to do is to input the x into the equation to find m<ABC
m<ABD=5x-4 m<DBC=3x+2 x=3 Given
m<ABD+m<DBC=m<ABC Angle Addition Postulate
5x-4+3x+2=m<ABC Substitution Property
5(3)-4+3(3)+2=m<ABC Substitution Property
15-4+9+2=m<ABC Distributive Property
22=m<ABC Simplify
x=6 M<ABC=22
m<ABD=5x-4 m<DBC=3x+2 Given
m<ABD+m<DBC=m<ABC Angle Addition Postulate
m<ABD=m<DBC Definition of Angle Bisection
5x+-4=3x+2 Substitution Property
2x-4=2 Subtraction Property
2x=6 Addition Property
x=3 Division Property
Now that we have found x the next thing to do is to input the x into the equation to find m<ABC
m<ABD=5x-4 m<DBC=3x+2 x=3 Given
m<ABD+m<DBC=m<ABC Angle Addition Postulate
5x-4+3x+2=m<ABC Substitution Property
5(3)-4+3(3)+2=m<ABC Substitution Property
15-4+9+2=m<ABC Distributive Property
22=m<ABC Simplify
x=6 M<ABC=22