BC bisects ABC. Solve for x and find mABC.
mABD= 8x-1, mCBD= 5x+5
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BD bisects ABC. Solve for x and find mABC.
mABD= 10x-6, mCBD= 6x+6
To solve for x, we can use the fact that BC bisects ABC. By definition, the angle measures on either side of the bisector are equal.
mABD = mCBD (By the angle bisector theorem)
8x - 1 = 5x + 5 (Substituting the given angle measures)
Now, let's solve for x:
8x - 1 = 5x + 5
Subtract 5x from both sides:
8x - 5x - 1 = 5x - 5x + 5
3x - 1 = 5
Add 1 to both sides:
3x - 1 + 1 = 5 + 1
3x = 6
Divide both sides by 3:
3x/3 = 6/3
x = 2
Therefore, x = 2.
To find mABC, substitute x = 2 into one of the given angle measures:
mABD = 8x - 1
mABD = 8(2) - 1
mABD = 16 - 1
mABD = 15
So, mABC = mABD = 15.
To solve for x, we can set the two angle measurements equal to each other.
mABD = mCBD
8x - 1 = 5x + 5
To isolate x, let's subtract 5x from both sides:
8x - 5x - 1 = 5x - 5x + 5
3x - 1 = 5
Now, let's add 1 to both sides:
3x - 1 + 1 = 5 + 1
3x = 6
Finally, divide both sides by 3 to solve for x:
3x/3 = 6/3
x = 2
Therefore, x = 2.
To find mABC, we can substitute the value of x into one of the given angle measurements:
mABD = 8x - 1
mABD = 8(2) - 1
mABD = 16 - 1
mABD = 15
Therefore, mABC is equal to 15 degrees.
How can BC bisect ABC? I guess you mean BD.
If it bisects the angle, then the two halves are equal. So,
8x-1 = 5x+5
x=2