Problem 7
Lynn Palmer
m<ABC=m<CBD and m<CBD=m<ABD. <ABC=3x-10. <ABD=8x-30. Find the value of x.
Because we know that m<ABC=m<CBD and m<CBD=m<ABD, we can conclude that m<ABD=m<ABD because of the transitive property. We can then use the substitution property on the next piece of information, which tells us that <ABC=3x-10 and <ABD=8x-30. If we substitute those values in the place of <ABC and <ABD, we would get 3x-5=8x-30. After that, we can solve for x to get the value of x.
Statement: Reason:
m<ABC=m<CBD Given
m<CBD=m<ABD
<ABC=3x-10
<ABD=8x-30
m<ABC=m<ABD Transitive Property
3x-10=8x-30 Substitution
-5x-10=-30 Subtraction Property of Equality
-5x=-20 Addition Property of Equality
x=4 Division Property of Equality
Because we know that m<ABC=m<CBD and m<CBD=m<ABD, we can conclude that m<ABD=m<ABD because of the transitive property. We can then use the substitution property on the next piece of information, which tells us that <ABC=3x-10 and <ABD=8x-30. If we substitute those values in the place of <ABC and <ABD, we would get 3x-5=8x-30. After that, we can solve for x to get the value of x.
Statement: Reason:
m<ABC=m<CBD Given
m<CBD=m<ABD
<ABC=3x-10
<ABD=8x-30
m<ABC=m<ABD Transitive Property
3x-10=8x-30 Substitution
-5x-10=-30 Subtraction Property of Equality
-5x=-20 Addition Property of Equality
x=4 Division Property of Equality