-->BD bisets angle ABC. Solve for x and find m angle ABC.
M angle ABD=7x-7, M angle CBD=4x+5
Since bisects angle ABC, angle ABD is congruent to angle CBD:
m angle ABD = m angle CBD
7x - 7 = 4x + 5
Subtract 4x from both sides:
7x - 4x - 7 = 4x - 4x + 5
3x - 7 = 5
Add 7 to both sides:
3x - 7 + 7 = 5 + 7
3x = 12
Divide by 3:
3x/3 = 12/3
x = 4
To find the measure of angle ABC, substitute the value of x into either angle ABD or angle CBD:
m angle ABC = m angle ABD = 7x - 7 = 7(4) - 7 = 28 - 7 = 21
Therefore, m angle ABC = 21.