BD is the bisector of angleABC. mangleABD= 7x+ 2 and mangle2(46-x). Find mangleABC, mangleDBC, mangleABD

Question

this is geometry, my teacher never taught this and i’m so lost

Answer 1

since BD bisects the larger angle ABC just set

ABD=DBC

7x+2 = 46-x

then solve for x

8x = 44

x =44/8= 11/2 =5.5

7x+2 = 7(5.5)+2 = 38.5+2 = 40.5 degrees = angle ABD

46-x = 46-5.5 = 40.5 degrees = angle DBC

angle ABC = 2(40.5) = or angles ABD+DBC = 40.5+40.5 = 81 degrees