Question

I need to know how to answer problems 11 and 12

Answer 1

#10:
since those two angles are supplementary then the line is equal to 180 degrees. so your equation would be:
(4x+10)+(x+20)=180
add common terms:
5x+30=180
subtract 30 from both sides to have the term with x alone, on one side of the equation:
5x=150
divide both sides to find the value of x and your answer is:
x=30

#11:
Since ray BD bisects angle ABC then angles ABD and DBC are equivalent to each other so your equation would be:
ABD=DBC
2x+10=x+20
Solve for x by adding x to both sides and also subtracting 10 from both sides:
x=10
Now to find the measure of angle EBA you must first find the measure of ABC to subtract that from the measure of EBC, which is 180 degrees.
So to find ABC:
ABD+DBC=ABC
2(10)+10+10+20=ABC
60=ABC

Now:
EBC-ABC=EBA
180-60=EBA
120=EBA