BD bisects ABC m ABC=9x. M ABD= 4x+38. Find m DBC
since BD bisects ABC, mABD = mDBC, and they add up to mABC:
9x = 2(4x+38)
To find the measure of angle DBC, we can use the fact that the sum of the angles in a triangle is 180 degrees.
First, we need to find the measure of angle ABC. We are given that BD bisects angle ABC, which means that angle ABD and angle DBC are equal in measure.
Let's set up an equation using the given information:
mABD = 4x + 38
mDBC = 4x + 38 (Since BD bisects ABC)
We know that the sum of the angles in a triangle is 180 degrees, so we can write the equation:
mABC + mABD + mDBC = 180
Substituting the given values into the equation, we have:
9x + (4x + 38) + (4x + 38) = 180
Simplifying the equation, we have:
9x + 4x + 38 + 4x + 38 = 180
17x + 76 = 180
Next, let's solve for x by isolating the variable:
17x = 180 - 76
17x = 104
x = 104/17 ≈ 6.12
Now, let's find the measure of angle DBC by substituting the value of x back into the equation:
mDBC = 4x + 38
mDBC = 4(6.12) + 38
mDBC = 24.48 + 38
mDBC ≈ 62.48
Therefore, the measure of angle DBC is approximately 62.48 degrees.