Question 151781
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+ABD=80+10}}}
{{{cross(3)ABD/cross(3)=cross(90)30/cross(3)}}}
{{{ABD=30deg}}}
Go back eqn 2:
{{{CBD=80-30}}}
{{{CBD=50deg}}} -----------------> FINAL ANSWER
IN doubt? go back eqn 1:
{{{50=2(30)-10}}}
{{{50=60-10}}}
{{{50=50}}} cool,
Thank you,
Jojo