BD bisects ABC. Solve for x and find mABC.
mABD= 10x-6, mCBD= 6x+6
Since BD bisects ABC, mABD = mCBD. Therefore, we can equate the two expressions:
10x - 6 = 6x + 6
Simplifying the equation:
4x = 12
Dividing both sides by 4:
x = 3
To find mABC, substitute x = 3 into either mABD or mCBD:
mABD = 10(3) - 6 = 30 - 6 = 24
Therefore, mABC = 2mABD = 2(24) = 48
Since BD bisects ABC, it divides angle ABC into two equal angles. Let's set the measures of these two angles equal to each other and solve for x.
mABD = mCBD
10x - 6 = 6x + 6
To solve for x, we need to isolate it on one side of the equation. Let's subtract 6x from both sides:
10x - 6x - 6 = 6x - 6x + 6
4x - 6 = 6
Next, let's add 6 to both sides:
4x - 6 + 6 = 6 + 6
4x = 12
Dividing both sides by 4:
4x/4 = 12/4
x = 3
Now that we have the value of x, we can substitute it back into either equation to find the measure of angle ABD.
mABD = 10x - 6
mABD = 10(3) - 6
mABD = 30 - 6
mABD = 24
Therefore, x = 3 and mABD = 24.
To find mABC, we can substitute the value of x back into either equation:
mCBD = 6x + 6
mCBD = 6(3) + 6
mCBD = 18 + 6
mCBD = 24
Therefore, mABC = mABD + mCBD = 24 + 24 = 48.