Answer:
[tex]x=5^o[/tex]
[tex]m\angle EBD=50^o[/tex]
Step-by-step explanation:
First case: angleEBD = 86 degrees, and angleDBC = 7 x + 8
Since BD bisects angleEBC, then angleDBC = 86/2 degrees = 43 degrees
then 43 = 7 x + 8
solving for "x":
43 - 8 = 7 x
35 = 7 x
dividing both sides by 7:
x = 5 degrees
Second case: angleEBD = 5 x + 20 and angleDBC = 7 x + 8
Since both angles must be of the same measure because BC is the bisector, then we can write the equation:
5 x + 20 = 7 x + 8
solve for x:
20 = 7 x - 5 x + 8
20 - 8 = 2 x
12 = 2 x
x = 6 degrees
now use x = 6 degrees to find angle EBD:
angleEBD = 5 (6) + 20 = 30 + 20 = 50 degrees.
