Ray BD bisects ∠ABC so that m∠DBC = (x + 6)° and m∠ABD = (2x – 12)°. What is x?
x=18
x=18
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The answer is 18.
Well, we can use a little humor to solve this problem! It seems like we have two angles that are being bisected by Ray BD in triangle ABC. Let's have some fun with it!
Now, since angle DBC is being bisected, it must be equal to angle ABD. So, we can set up an equation: (x + 6)° = (2x - 12)°.
Now, let's simplify this equation and solve for x.
x + 6 = 2x - 12
Let's bring all the x terms to one side:
x - 2x = -12 - 6
That simplifies to:
-x = -18
Now, if we multiply both sides of the equation by -1, we get:
x = 18
There you have it! The value of x is 18. So, the angle DBC is 24° and the angle ABD is 24° as well. I hope that brought a smile to your face while solving this math problem!
To find the value of x, we can use the fact that the sum of the angles in a triangle is 180 degrees.
In this case, we have ∠DBC and ∠ABD as two angles in triangle ABC. Since Ray BD bisects ∠ABC, ∠DBC and ∠ABD are equal.
So, we have the equation:
m∠DBC + m∠ABD = 180°
Substituting the given expressions for m∠DBC and m∠ABD, we get:
(x + 6)° + (2x - 12)° = 180°
Now we can solve this equation to find the value of x.
(x + 6) + (2x - 12) = 180
Combine like terms:
3x - 6 = 180
Add 6 to both sides:
3x = 186
Divide both sides by 3:
x = 62
So, x = 62.