SOLUTION: a. The measure of angle CBD is 10 less than twice the measure of angle ABD. If D is in the interior of angle ABC and the measure of angle ABC is 80, what is the measure of angle CB

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: a. The measure of angle CBD is 10 less than twice the measure of angle ABD. If D is in the interior of angle ABC and the measure of angle ABC is 80, what is the measure of angle CB      Log On

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Question 151781: a. The measure of angle CBD is 10 less than twice the measure of angle ABD. If D is in the interior of angle ABC and the measure of angle ABC is 80, what is the measure of angle CBD?
Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!
We take the 1st condition: a. The measure of angle CBD is 10 less than twice the measure of angle ABD.
CBD=2ABD-10 -----------------------> eqn 1
Since D is in the interior of angle ABC, there forms an angle ABD right? Therefore, angle CBD=ABC-ABD, see the correlation there?
It's better you draw it to follow the interpretation better.
Since ABC=80deg, then CBD=80-ABD ---------------------> eqn 2
.
Equating the 2 eqns:
2ABD-10=80-ABD
2ABD%2BABD=80%2B10
cross%283%29ABD%2Fcross%283%29=cross%2890%2930%2Fcross%283%29
ABD=30deg
Go back eqn 2:
CBD=80-30
CBD=50deg -----------------> FINAL ANSWER
IN doubt? go back eqn 1:
50=2%2830%29-10
50=60-10
50=50 cool,
Thank you,
Jojo