Algebra BD bisects <ABC. Solve for x and find m<ABC.
m<ABD = 4x - 16, m<CBD = 2x + 6
Please teach me how to work this.
since BD bisects <ABC, m<ABD = m<DBC
4x-16 = 2x+6
2x = 22
x = 11
m<ABC = m<ABD + m<DBC = 4*11-16 + 2*11+6 = 28+28 = 56
Steve, thank you so much. You explained it so I could understand it.
That's the plan. :-)
in triangle ABC, BD bisects <ABC, <ABD = 4x + 6 and m<DBC = 5x -5. find the m<abc
bisects ∠ABC, m∠ABD = (6x − 8)°, and m∠CBD = (2x + 28)°. What is m∠ABC?
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To solve for x and find the measure of angle ABC, we can use the fact that angle ABD and angle CBD are bisected by the line BD.
Since angle ABD and angle CBD are bisected, their measures are equal. We can set up an equation using the given information:
m<ABD = m<CBD
4x - 16 = 2x + 6
To solve for x, we need to isolate the variable x on one side of the equation. Let's start by moving the terms with x to one side and the constant terms to the other side:
4x - 2x = 6 + 16
2x = 22
Now, we can solve for x by dividing both sides of the equation by 2:
2x/2 = 22/2
x = 11
So, x is equal to 11.
To find the measure of angle ABC, we can substitute the value of x back into one of the given equations. Let's use m<ABD = 4x - 16:
m<ABD = 4(11) - 16
m<ABD = 44 - 16
m<ABD = 28
Therefore, the measure of angle ABC is 28 degrees.