In the figure, ->
BD is the angle bisector of <ABC. If <ABD= 3x+2 and m<ABC=7x-6, find the degree measure of <CBD
A
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B--- D
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C
How to solve 2x(3x-x)=0?
2x (2x) =0. 2x =0. X =0
To find the degree measure of <CBD, we first need to use the given information about angle bisectors.
Since BD is the angle bisector of <ABC, it divides the angle <ABC into two equal halves, <ABD and <CBD.
We are given that <ABD = 3x + 2 and <ABC = 7x - 6.
Since <ABD and <CBD are equal halves of <ABC, we can set up an equation:
3x + 2 = 7x - 6
To solve for x, we can simplify the equation:
3x - 7x = -6 - 2
-4x = -8
Dividing both sides by -4, we get:
x = 2
Now that we have found the value of x, we can substitute it back into either <ABD or <ABC to find the respective angle measure.
Using <ABD = 3x + 2, we substitute x = 2:
<ABD = 3(2) + 2
<ABD = 6 + 2
<ABD = 8
So, the degree measure of <ABD is 8 degrees.
Since <ABD and <CBD are equal halves of <ABC, the degree measure of <CBD is also 8 degrees.