Ray BD bisects angle ABC. The measure of angle ABD is represented by 4x-4 and the measure of angle ABC is represented by 7x+4. Find the measures of angle DBC.
2006-08-25 09:41:25 · 6 answers · asked by Roberta A 1 in Science & Mathematics ➔ Mathematics
ABD = 4x - 4
ABC = 7x+4
when Ray BD bisects angle ABC it means ABC is bisected ; 2 ABD = ABC and ABD = DBC = 4x - 4
2*(4x-4) = 7x+4
8x - 8 = 7x +4
8x - 7x + 4+8
x=12
ABC = 7x+4 = 7 * 12 + 4= 88
ABD =DBC = 4x - 4 = 4*12-4 = 44
2006-08-25 10:45:06 · answer #1 · answered by sweetie 5 · 1⤊ 0⤋
Ray BD bisects angle ABC.
Here, we have two equations
With the Angle Addition Postulate,
angle ABD + angle DBC = angle ABC
With the Definition of an Angle Bisector,
angle ABD = angle DBC
Since it is also given that
angle ABD = 4x - 4 and
angle ABC = 7x + 4
Therefore,
angle DBC = angle ABD = 4x - 4
and
(4x - 4) + (4x - 4) = 7x + 4
8x - 8 = 7x + 4
8x - 7x = 4 + 8
x = 12
angle DBC = 4x - 4
angle DBC = 4(12) - 4
angle DBC = 48 - 4
angle DBC = 44
^_^
2006-08-26 06:11:58 · answer #2 · answered by kevin! 5 · 0⤊ 0⤋
ang. ABD=4x-4, ang. ABC= 7x+4
angle is bisected, so abc=2(abd)
7x+4 = 8x-8
12= x
ang. ABD=44
ryt???
2006-08-25 16:53:30 · answer #3 · answered by prasad c 1 · 0⤊ 0⤋
Bisects means cuts in half. You know the whole quantity, and you know one half of the quantity. You can then solve for x, and then plug it in to 4x-4 to get your answer. Which should be 2 more than the meaning of life, the universe, and everything.
2006-08-25 16:47:42 · answer #4 · answered by zex20913 5 · 0⤊ 0⤋
Roberta:
Girl, you have asked a dozen math questions (maybe more) in just the last 2 days. You need to seriously consider getting off your computer, and opening that math book. For real!
2006-08-25 18:01:10 · answer #5 · answered by Carlos R 5 · 0⤊ 0⤋
4x - 4 = 7x + 4
Do your own homework, solve for x and then plug x into one of the equations ( doesn't matter which since they're both equal )
Isolate x, then you should know what to do...
2006-08-25 16:46:18 · answer #6 · answered by ? 3 · 0⤊ 0⤋